Index: src/main/org/codehaus/groovy/transform/ImmutableASTTransformation.java
===================================================================
--- src/main/org/codehaus/groovy/transform/ImmutableASTTransformation.java  (revision 17485)
+++ src/main/org/codehaus/groovy/transform/ImmutableASTTransformation.java  (working copy)
@@ -91,6 +91,12 @@
         if (parent instanceof ClassNode) {
             ClassNode cNode = (ClassNode) parent;
             String cName = cNode.getName();
+            if(hasDeclaredMethod(cNode, "equals", 1)) {
+                throw new RuntimeException("Classes marked @Immutable cannot override equals().");
+            }
+            if(hasDeclaredMethod(cNode, "hashCode", 0)) {
+                throw new RuntimeException("Classes marked @Immutable cannot override hashCode().");
+            }
             if (cNode.isInterface()) {
                 throw new RuntimeException("Error processing interface '" + cName + "'. " + MY_TYPE_NAME + " not allowed for interfaces.");
             }
@@ -113,9 +119,22 @@
             createConstructor(cNode);
             createHashCode(cNode);
             createEquals(cNode);
-            createToString(cNode);
+            if(!hasDeclaredMethod(cNode, "toString", 0)) {
+                createToString(cNode);
+            }
         }
     }
+
+    private boolean hasDeclaredMethod(ClassNode cNode, String name, int argsCount) {
+        List<MethodNode> ms = cNode.getDeclaredMethods(name);
+        for(MethodNode m : ms) {
+           Parameter[] paras = m.getParameters();
+           if(paras != null && paras.length == argsCount) {
+                return true;
+           }
+        }
+        return false;
+    }

     private void ensureNotPublic(String cNode, FieldNode fNode) {
         String fName = fNode.getName();
Index: src/test/groovy/bugs/Groovy3713Bug.groovy
===================================================================
--- src/test/groovy/bugs/Groovy3713Bug.groovy   (revision 0)
+++ src/test/groovy/bugs/Groovy3713Bug.groovy   (revision 0)
@@ -0,0 +1,50 @@
+package groovy.bugs
+
+import gls.CompilableTestSupport
+
+class Groovy3713Bug extends CompilableTestSupport {
+    void testOverridingObjectMethodsWithImmutable() {
+       // overriding of standard toString - allowed
+        assertScript """
+           @Immutable class MyClass {
+               String toString() { 'some return value' }
+           }
+           new MyClass()
+        """
+        // overriding hashCode() - not allowed
+        shouldFail """
+           @Immutable class MyClass {
+               int hashCode() {0}
+           }
+           new MyClass()
+        """
+        // overloaded hashCode() - allowed
+        assertScript """
+            @Immutable class MyClass {
+                int hashCode(tmp) {tmp}
+            }
+            new MyClass()
+        """
+        // overriding equals() - not allowed
+       shouldFail """
+            @Immutable class MyClass {
+                boolean equals(obj) {true}
+            }
+            new MyClass()
+        """
+        // overriding equals() - not allowed
+        shouldFail """
+            @Immutable class MyClass {
+                boolean equals(MyClass obj) {true}
+            }
+            new MyClass()
+        """
+        // overloaded equals() - allowed
+        assertScript """
+            @Immutable class MyClass {
+                boolean equals(MyClass obj, MyClass obj1) {true}
+            }
+            new MyClass()
+        """
+    }
+}
\ No newline at end of file