diff --git a/core/src/analyzer/compound_assignments.rs b/core/src/analyzer/compound_assignments.rs
new file mode 100644
index 0000000..1d56395
--- /dev/null
+++ b/core/src/analyzer/compound_assignments.rs
@@ -0,0 +1,194 @@
+//! Compound assignment handlers (`x += 1`, `x ||= val`, `x &&= val`).
+//!
+//! `||=` and `&&=` use the same Union(existing, val) approximation — a sound
+//! over-approximation without condition narrowing.
+
+use crate::env::{GlobalEnv, LocalEnv};
+use crate::graph::{ChangeSet, VertexId};
+use crate::types::Type;
+
+use super::calls::install_method_call;
+use super::variables::{
+    install_class_var_read, install_class_var_write, install_constant_read, install_constant_write,
+    install_global_var_read, install_global_var_write, install_ivar_read, install_ivar_write,
+    install_local_var_read, install_local_var_write,
+};
+
+pub(crate) enum CompoundVarKind {
+    Local(String),
+    Ivar(String),
+    ClassVar(String),
+    GlobalVar(String),
+    Constant(String),
+}
+
+impl CompoundVarKind {
+    fn read(&self, genv: &GlobalEnv, lenv: &LocalEnv) -> Option<VertexId> {
+        match self {
+            Self::Local(name) => install_local_var_read(lenv, name),
+            Self::Ivar(name) => install_ivar_read(genv, name),
+            Self::ClassVar(name) => install_class_var_read(genv, name),
+            Self::GlobalVar(name) => install_global_var_read(genv, name),
+            Self::Constant(name) => install_constant_read(genv, name),
+        }
+    }
+
+    fn write(
+        self,
+        genv: &mut GlobalEnv,
+        lenv: &mut LocalEnv,
+        changes: &mut ChangeSet,
+        value_vtx: VertexId,
+    ) -> VertexId {
+        match self {
+            Self::Local(name) => install_local_var_write(genv, lenv, changes, name, value_vtx),
+            Self::Ivar(name) => install_ivar_write(genv, name, value_vtx),
+            Self::ClassVar(name) => install_class_var_write(genv, name, value_vtx),
+            Self::GlobalVar(name) => install_global_var_write(genv, name, value_vtx),
+            Self::Constant(name) => install_constant_write(genv, name, value_vtx),
+        }
+    }
+}
+
+pub(crate) enum CompoundOp {
+    Operator(String),
+    Logical,
+}
+
+pub(crate) fn process_compound_write(
+    genv: &mut GlobalEnv,
+    lenv: &mut LocalEnv,
+    changes: &mut ChangeSet,
+    var_kind: CompoundVarKind,
+    op: CompoundOp,
+    value_vtx: VertexId,
+) -> VertexId {
+    match op {
+        CompoundOp::Operator(operator) => {
+            let current_vtx = var_kind.read(genv, lenv)
+                .unwrap_or_else(|| genv.new_source(Type::Nil));
+            let result_vtx = install_method_call(
+                genv, current_vtx, operator, vec![value_vtx], None, None, false,
+            );
+            var_kind.write(genv, lenv, changes, result_vtx)
+        }
+        CompoundOp::Logical => {
+            let merge_vtx = genv.new_vertex();
+            if let Some(current_vtx) = var_kind.read(genv, lenv) {
+                genv.add_edge(current_vtx, merge_vtx);
+            }
+            genv.add_edge(value_vtx, merge_vtx);
+            var_kind.write(genv, lenv, changes, merge_vtx)
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_operator_write() {
+        let mut genv = GlobalEnv::new();
+        let mut lenv = LocalEnv::new();
+        let mut changes = ChangeSet::new();
+
+        let int_vtx = genv.new_source(Type::integer());
+        install_local_var_write(&mut genv, &mut lenv, &mut changes, "x".to_string(), int_vtx);
+
+        let rhs_vtx = genv.new_source(Type::integer());
+        let result = process_compound_write(
+            &mut genv, &mut lenv, &mut changes,
+            CompoundVarKind::Local("x".to_string()),
+            CompoundOp::Operator("+".to_string()),
+            rhs_vtx,
+        );
+
+        assert_ne!(result, int_vtx);
+        assert_eq!(install_local_var_read(&lenv, "x"), Some(result));
+    }
+
+    #[test]
+    fn test_operator_write_uninitialized() {
+        let mut genv = GlobalEnv::new();
+        let mut lenv = LocalEnv::new();
+        let mut changes = ChangeSet::new();
+
+        let rhs_vtx = genv.new_source(Type::integer());
+        let result = process_compound_write(
+            &mut genv, &mut lenv, &mut changes,
+            CompoundVarKind::Local("x".to_string()),
+            CompoundOp::Operator("+".to_string()),
+            rhs_vtx,
+        );
+
+        assert_eq!(install_local_var_read(&lenv, "x"), Some(result));
+    }
+
+    #[test]
+    fn test_logical_write_produces_union() {
+        let mut genv = GlobalEnv::new();
+        let mut lenv = LocalEnv::new();
+        let mut changes = ChangeSet::new();
+
+        let str_vtx = genv.new_source(Type::string());
+        install_local_var_write(&mut genv, &mut lenv, &mut changes, "x".to_string(), str_vtx);
+
+        let int_vtx = genv.new_source(Type::integer());
+        let result = process_compound_write(
+            &mut genv, &mut lenv, &mut changes,
+            CompoundVarKind::Local("x".to_string()),
+            CompoundOp::Logical,
+            int_vtx,
+        );
+
+        assert_eq!(install_local_var_read(&lenv, "x"), Some(result));
+        genv.apply_changes(changes);
+        genv.run_all();
+        let types = genv.get_receiver_types(result).unwrap();
+        assert!(types.contains(&Type::string()));
+        assert!(types.contains(&Type::integer()));
+    }
+
+    #[test]
+    fn test_logical_write_uninitialized() {
+        let mut genv = GlobalEnv::new();
+        let mut lenv = LocalEnv::new();
+        let mut changes = ChangeSet::new();
+
+        let str_vtx = genv.new_source(Type::string());
+        let result = process_compound_write(
+            &mut genv, &mut lenv, &mut changes,
+            CompoundVarKind::Local("x".to_string()),
+            CompoundOp::Logical,
+            str_vtx,
+        );
+
+        genv.apply_changes(changes);
+        genv.run_all();
+        let types = genv.get_receiver_types(result).unwrap();
+        assert!(types.contains(&Type::string()));
+    }
+
+    #[test]
+    fn test_ivar_compound_write() {
+        let mut genv = GlobalEnv::new();
+        let mut lenv = LocalEnv::new();
+        let mut changes = ChangeSet::new();
+        genv.enter_class("TestClass".to_string(), None);
+        genv.enter_method("test_method".to_string());
+
+        let int_vtx = genv.new_source(Type::integer());
+        install_ivar_write(&mut genv, "@count".to_string(), int_vtx);
+
+        let rhs_vtx = genv.new_source(Type::integer());
+        let result = process_compound_write(
+            &mut genv, &mut lenv, &mut changes,
+            CompoundVarKind::Ivar("@count".to_string()),
+            CompoundOp::Operator("+".to_string()),
+            rhs_vtx,
+        );
+
+        assert_eq!(result, int_vtx);
+    }
+}
diff --git a/core/src/analyzer/dispatch.rs b/core/src/analyzer/dispatch.rs
index c2c381f..fa95d61 100644
--- a/core/src/analyzer/dispatch.rs
+++ b/core/src/analyzer/dispatch.rs
@@ -13,6 +13,7 @@ use ruby_prism::Node;
 
 use super::bytes_to_name;
 use super::calls::install_method_call;
+use super::compound_assignments::{CompoundOp, CompoundVarKind};
 use super::variables::{
     install_class_var_read, install_class_var_write, install_constant_read, install_constant_write,
     install_global_var_read, install_global_var_write, install_ivar_read, install_ivar_write,
@@ -85,6 +86,11 @@ pub(crate) enum NeedsChildKind<'a> {
     /// Global variable write: need to process value, then call install_global_var_write
     GlobalVarWrite { gvar_name: String, value: Node<'a> },
     ConstantWrite { const_name: String, value: Node<'a> },
+    CompoundWrite {
+        var_kind: CompoundVarKind,
+        op: CompoundOp,
+        value: Node<'a>,
+    },
     /// Proc/lambda literals
     ProcLiteral { block: Node<'a> },
     /// Method call: need to process receiver, then call finish_method_call
@@ -281,6 +287,46 @@ pub(crate) fn dispatch_needs_child<'a>(node: &Node<'a>, source: &str) -> Option<
         });
     }
 
+    macro_rules! dispatch_compound {
+        ($node:expr, $as_method:ident, $var_kind:ident, operator) => {
+            if let Some(n) = $node.$as_method() {
+                return Some(NeedsChildKind::CompoundWrite {
+                    var_kind: CompoundVarKind::$var_kind(bytes_to_name(n.name().as_slice())),
+                    op: CompoundOp::Operator(bytes_to_name(n.binary_operator().as_slice())),
+                    value: n.value(),
+                });
+            }
+        };
+        ($node:expr, $as_method:ident, $var_kind:ident, $op:ident) => {
+            if let Some(n) = $node.$as_method() {
+                return Some(NeedsChildKind::CompoundWrite {
+                    var_kind: CompoundVarKind::$var_kind(bytes_to_name(n.name().as_slice())),
+                    op: CompoundOp::$op,
+                    value: n.value(),
+                });
+            }
+        };
+    }
+
+    macro_rules! dispatch_compound_all {
+        ($node:expr, $op_method:ident, $or_method:ident, $and_method:ident, $var_kind:ident) => {
+            dispatch_compound!($node, $op_method, $var_kind, operator);
+            dispatch_compound!($node, $or_method, $var_kind, Logical);
+            dispatch_compound!($node, $and_method, $var_kind, Logical);
+        };
+    }
+
+    dispatch_compound_all!(node,
+        as_local_variable_operator_write_node, as_local_variable_or_write_node, as_local_variable_and_write_node, Local);
+    dispatch_compound_all!(node,
+        as_instance_variable_operator_write_node, as_instance_variable_or_write_node, as_instance_variable_and_write_node, Ivar);
+    dispatch_compound_all!(node,
+        as_class_variable_operator_write_node, as_class_variable_or_write_node, as_class_variable_and_write_node, ClassVar);
+    dispatch_compound_all!(node,
+        as_global_variable_operator_write_node, as_global_variable_or_write_node, as_global_variable_and_write_node, GlobalVar);
+    dispatch_compound_all!(node,
+        as_constant_operator_write_node, as_constant_or_write_node, as_constant_and_write_node, Constant);
+
     // Method call: x.upcase, x.each { |i| ... }, or name (implicit self)
     if let Some(call_node) = node.as_call_node() {
         let method_name = bytes_to_name(call_node.name().as_slice());
@@ -403,6 +449,12 @@ pub(crate) fn process_needs_child(
             let value_vtx = super::install::install_node(genv, lenv, changes, source, &value)?;
             Some(install_local_var_write(genv, lenv, changes, var_name, value_vtx))
         }
+        NeedsChildKind::CompoundWrite { var_kind, op, value } => {
+            let value_vtx = super::install::install_node(genv, lenv, changes, source, &value)?;
+            Some(super::compound_assignments::process_compound_write(
+                genv, lenv, changes, var_kind, op, value_vtx,
+            ))
+        }
         NeedsChildKind::ProcLiteral { block } => {
             if let Some(block_node) = block.as_block_node() {
                 super::lambdas::process_block_as_proc(genv, lenv, changes, source, &block_node)
diff --git a/core/src/analyzer/mod.rs b/core/src/analyzer/mod.rs
index ff8a925..d2858d5 100644
--- a/core/src/analyzer/mod.rs
+++ b/core/src/analyzer/mod.rs
@@ -2,6 +2,7 @@ mod assignments;
 mod attributes;
 mod blocks;
 mod calls;
+mod compound_assignments;
 mod conditionals;
 mod definitions;
 mod exceptions;
diff --git a/test/compound_assignment_test.rb b/test/compound_assignment_test.rb
new file mode 100644
index 0000000..ed51ffa
--- /dev/null
+++ b/test/compound_assignment_test.rb
@@ -0,0 +1,171 @@
+# frozen_string_literal: true
+
+require 'test_helper'
+
+class CompoundAssignmentTest < Minitest::Test
+  include CLITestHelper
+
+  # ============================================
+  # No Error
+  # ============================================
+
+  def test_local_operator_assign_no_error
+    source = <<~RUBY
+      class Foo
+        def bar
+          x = 1
+          x += 2
+          x.even?
+        end
+      end
+    RUBY
+
+    assert_no_check_errors(source)
+  end
+
+  def test_local_or_assign_no_error
+    source = <<~RUBY
+      class Foo
+        def bar
+          x = "hello"
+          x ||= "world"
+          x.upcase
+        end
+      end
+    RUBY
+
+    assert_no_check_errors(source)
+  end
+
+  def test_local_or_assign_no_error_without_initialization
+    source = <<~RUBY
+      class Foo
+        def bar
+          x ||= "world"
+          x.upcase
+        end
+      end
+    RUBY
+
+    assert_no_check_errors(source)
+  end
+
+  def test_local_and_assign_no_error
+    source = <<~RUBY
+      class Foo
+        def bar
+          x = "hello"
+          x &&= "world"
+          x.upcase
+        end
+      end
+    RUBY
+
+    assert_no_check_errors(source)
+  end
+
+  def test_ivar_operator_assign_no_error
+    source = <<~RUBY
+      class Counter
+        def initialize
+          @count = 0
+        end
+
+        def increment
+          @count += 1
+        end
+
+        def value
+          @count.even?
+        end
+      end
+    RUBY
+
+    assert_no_check_errors(source)
+  end
+
+  def test_ivar_or_assign_no_error
+    source = <<~RUBY
+      class Config
+        def initialize
+          @name = "default"
+        end
+
+        def set_name
+          @name ||= "fallback"
+        end
+
+        def display
+          @name.upcase
+        end
+      end
+    RUBY
+
+    assert_no_check_errors(source)
+  end
+
+  # ============================================
+  # Error Detection
+  # ============================================
+
+  def test_operator_assign_type_error
+    source = <<~RUBY
+      class Foo
+        def bar
+          x = 1
+          x += 2
+          x.upcase
+        end
+      end
+    RUBY
+
+    assert_check_error(source, method_name: 'upcase', receiver_type: 'Integer')
+  end
+
+  def test_or_assign_type_error
+    source = <<~RUBY
+      class Foo
+        def bar
+          x = 1
+          x ||= "hello"
+          x.even?
+        end
+      end
+    RUBY
+
+    assert_check_error(source, method_name: 'even?', receiver_type: 'String')
+  end
+
+  def test_and_assign_type_error
+    source = <<~RUBY
+      class Foo
+        def bar
+          x &&= "hello"
+          x.even?
+        end
+      end
+    RUBY
+
+    assert_check_error(source, method_name: 'even?', receiver_type: 'String')
+  end
+
+  def test_ivar_operator_assign_type_error
+    source = <<~RUBY
+      class Counter
+        def initialize
+          @count = 0
+        end
+
+        def increment
+          @count += 1
+        end
+
+        def name
+          @count.upcase
+        end
+      end
+    RUBY
+
+    assert_check_error(source, method_name: 'upcase', receiver_type: 'Integer')
+  end
+end