diff --git a/compiler/frontend/src/org/jetbrains/kotlin/resolve/checkers/HeaderImplDeclarationChecker.kt b/compiler/frontend/src/org/jetbrains/kotlin/resolve/checkers/HeaderImplDeclarationChecker.kt
index 5645a53690b..76c5a9bd21c 100644
--- a/compiler/frontend/src/org/jetbrains/kotlin/resolve/checkers/HeaderImplDeclarationChecker.kt
+++ b/compiler/frontend/src/org/jetbrains/kotlin/resolve/checkers/HeaderImplDeclarationChecker.kt
@@ -16,6 +16,7 @@
 
 package org.jetbrains.kotlin.resolve.checkers
 
+import org.jetbrains.kotlin.builtins.KotlinBuiltIns
 import org.jetbrains.kotlin.config.LanguageFeature
 import org.jetbrains.kotlin.config.LanguageVersionSettings
 import org.jetbrains.kotlin.descriptors.*
@@ -258,7 +259,7 @@ class HeaderImplDeclarationChecker(val moduleToCheck: ModuleDescriptor? = null)
             else -> throw AssertionError("Unsupported declarations: $a, $b")
         }
 
-        if (checkImpl && !b.isImpl) return Incompatible.NoImpl
+        if (checkImpl && !b.isImpl && b.kind == CallableMemberDescriptor.Kind.DECLARATION) return Incompatible.NoImpl
 
         return Compatible
     }
@@ -323,7 +324,11 @@ class HeaderImplDeclarationChecker(val moduleToCheck: ModuleDescriptor? = null)
 
         areCompatibleTypeParameters(aTypeParams, bTypeParams, substitutor).let { if (it != Compatible) return it }
 
-        if (!b.typeConstructor.supertypes.containsAll(a.typeConstructor.supertypes.map(substitutor))) return Incompatible.Supertypes
+        // Subtract kotlin.Any from supertypes because it's implicitly added if no explicit supertype is specified,
+        // and not added if an explicit supertype _is_ specified
+        val aSupertypes = a.typeConstructor.supertypes.filterNot(KotlinBuiltIns::isAny)
+        val bSupertypes = b.typeConstructor.supertypes.filterNot(KotlinBuiltIns::isAny)
+        if (!bSupertypes.containsAll(aSupertypes.map(substitutor))) return Incompatible.Supertypes
 
         areCompatibleClassScopes(a, b, checkImpl && !implTypealias, substitutor).let { if (it != Compatible) return it }
 
diff --git a/compiler/testData/diagnostics/tests/multiplatform/implDelegatedMember.kt b/compiler/testData/diagnostics/tests/multiplatform/implDelegatedMember.kt
new file mode 100644
index 00000000000..59383edc573
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/multiplatform/implDelegatedMember.kt
@@ -0,0 +1,19 @@
+// !LANGUAGE: +MultiPlatformProjects
+// MODULE: m1-common
+// FILE: common.kt
+
+header open class Foo {
+    open fun bar(): String
+}
+
+// MODULE: m2-jvm(m1-common)
+// FILE: jvm.kt
+
+interface Bar {
+    fun bar(): String
+}
+
+val bar: Bar
+    get() = null!!
+
+impl open class Foo : Bar by bar
diff --git a/compiler/testData/diagnostics/tests/multiplatform/implDelegatedMember.txt b/compiler/testData/diagnostics/tests/multiplatform/implDelegatedMember.txt
new file mode 100644
index 00000000000..e39a55d5100
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/multiplatform/implDelegatedMember.txt
@@ -0,0 +1,31 @@
+// -- Module: <m1-common> --
+package
+
+public open header class Foo {
+    public constructor Foo()
+    public open header fun bar(): kotlin.String
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+
+// -- Module: <m2-jvm> --
+package
+
+public val bar: Bar
+
+public interface Bar {
+    public abstract fun bar(): kotlin.String
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+public open impl class Foo : Bar {
+    public constructor Foo()
+    public open override /*1*/ /*delegation*/ fun bar(): kotlin.String
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
diff --git a/compiler/testData/diagnostics/tests/multiplatform/implFakeOverride.kt b/compiler/testData/diagnostics/tests/multiplatform/implFakeOverride.kt
new file mode 100644
index 00000000000..e38b7c8596e
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/multiplatform/implFakeOverride.kt
@@ -0,0 +1,16 @@
+// !LANGUAGE: +MultiPlatformProjects
+// MODULE: m1-common
+// FILE: common.kt
+
+header class Foo {
+    fun bar(): String
+}
+
+// MODULE: m2-jvm(m1-common)
+// FILE: jvm.kt
+
+open class Bar {
+    fun bar() = "bar"
+}
+
+impl class Foo : Bar()
diff --git a/compiler/testData/diagnostics/tests/multiplatform/implFakeOverride.txt b/compiler/testData/diagnostics/tests/multiplatform/implFakeOverride.txt
new file mode 100644
index 00000000000..17e0002a910
--- /dev/null
+++ b/compiler/testData/diagnostics/tests/multiplatform/implFakeOverride.txt
@@ -0,0 +1,30 @@
+// -- Module: <m1-common> --
+package
+
+public final header class Foo {
+    public constructor Foo()
+    public final header fun bar(): kotlin.String
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+
+// -- Module: <m2-jvm> --
+package
+
+public open class Bar {
+    public constructor Bar()
+    public final fun bar(): kotlin.String
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
+
+public final impl class Foo : Bar {
+    public constructor Foo()
+    public final override /*1*/ /*fake_override*/ fun bar(): kotlin.String
+    public open override /*1*/ /*fake_override*/ fun equals(/*0*/ other: kotlin.Any?): kotlin.Boolean
+    public open override /*1*/ /*fake_override*/ fun hashCode(): kotlin.Int
+    public open override /*1*/ /*fake_override*/ fun toString(): kotlin.String
+}
diff --git a/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java b/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
index 9e85496a8ef..796f6ee32a7 100644
--- a/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
+++ b/compiler/tests/org/jetbrains/kotlin/checkers/DiagnosticsTestGenerated.java
@@ -13036,6 +13036,18 @@ public class DiagnosticsTestGenerated extends AbstractDiagnosticsTest {
                 KotlinTestUtils.assertAllTestsPresentByMetadata(this.getClass(), new File("compiler/testData/diagnostics/tests/multiplatform"), Pattern.compile("^(.+)\\.kt$"), TargetBackend.ANY, true);
             }
 
+            @TestMetadata("implDelegatedMember.kt")
+            public void testImplDelegatedMember() throws Exception {
+                String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/multiplatform/implDelegatedMember.kt");
+                doTest(fileName);
+            }
+
+            @TestMetadata("implFakeOverride.kt")
+            public void testImplFakeOverride() throws Exception {
+                String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/multiplatform/implFakeOverride.kt");
+                doTest(fileName);
+            }
+
             @TestMetadata("modifierApplicability.kt")
             public void testModifierApplicability() throws Exception {
                 String fileName = KotlinTestUtils.navigationMetadata("compiler/testData/diagnostics/tests/multiplatform/modifierApplicability.kt");