diff --git a/src/NSubstitute/Core/Extensions.cs b/src/NSubstitute/Core/Extensions.cs
index bb3a4880..608d98fa 100644
--- a/src/NSubstitute/Core/Extensions.cs
+++ b/src/NSubstitute/Core/Extensions.cs
@@ -23,18 +23,30 @@ public static bool IsCompatibleWith(this object? instance, Type type)
             return TypeCanBeNull(requiredType);
         }
 
-        var instanceType = instance.GetType();
+        var genericTypeDefinition = type.IsGenericType ? type.GetGenericTypeDefinition() : null;
 
-        if (instanceType.IsGenericType && type.IsGenericType
-                && instanceType.GetGenericTypeDefinition() == type.GetGenericTypeDefinition())
+        if (genericTypeDefinition is not null)
         {
-            // both are the same generic type. If their GenericTypeArguments match then they are equivalent 
-            return CallSpecification.TypesAreAllEquivalent(instanceType.GenericTypeArguments, type.GenericTypeArguments);
+            var instanceType = instance.GetType();
+            var compatibleInstanceTypes = GetCompatibleTypes(instanceType);
+
+            foreach (var aCompatibleInstanceType in compatibleInstanceTypes)
+            {
+                if (aCompatibleInstanceType.IsGenericType &&
+                    aCompatibleInstanceType.GetGenericTypeDefinition() == genericTypeDefinition)
+                {
+                    // both are the same generic type. If their GenericTypeArguments match then they are equivalent
+                    return CallSpecification.TypesAreAllEquivalent(
+                        aCompatibleInstanceType.GenericTypeArguments, type.GenericTypeArguments);
+                }
+            }
         }
 
         return requiredType.IsInstanceOfType(instance);
     }
 
+    private static IReadOnlyList<Type> GetCompatibleTypes(Type type) => [type, .. type.GetInterfaces()];
+
     /// <summary>
     /// Join the <paramref name="strings"/> using <paramref name="separator"/>.
     /// </summary>
diff --git a/tests/NSubstitute.Acceptance.Specs/ArgumentMatching.cs b/tests/NSubstitute.Acceptance.Specs/ArgumentMatching.cs
index 23151337..8b131553 100644
--- a/tests/NSubstitute.Acceptance.Specs/ArgumentMatching.cs
+++ b/tests/NSubstitute.Acceptance.Specs/ArgumentMatching.cs
@@ -300,11 +300,11 @@ public void Should_allow_to_check_received_using_properties_from_other_substitut
     public void Throw_with_ambiguous_arguments_when_given_an_arg_matcher_and_a_default_arg_value_v1()
     {
         Assert.Throws<AmbiguousArgumentsException>(() =>
-           {
-               _something.Add(0, Arg.Any<int>()).Returns(1);
-               Assert.Fail("Should not make it here, as it can't work out which arg the matcher refers to." +
-                           "If it does this will throw an AssertionException rather than AmbiguousArgumentsException.");
-           });
+        {
+            _something.Add(0, Arg.Any<int>()).Returns(1);
+            Assert.Fail("Should not make it here, as it can't work out which arg the matcher refers to." +
+                        "If it does this will throw an AssertionException rather than AmbiguousArgumentsException.");
+        });
     }
 
     [Test]
@@ -740,9 +740,109 @@ public void Supports_custom_argument_matcher_descriptions()
         Assert.That(ex.Message, Contains.Substring("24 is not forty two"));
     }
 
+    [Test]
+    public void Supports_matching_generic_interface_bound_type_string_with_class_argument()
+    {
+        var service = Substitute.For<IMyService>();
+        var argument = new MyStringArgument();
+
+        service.MyMethod(argument);
+
+        service.Received().MyMethod(Arg.Any<IMyArgument<string>>());
+    }
+
+    [Test]
+    public void Supports_matching_generic_interface_bound_type_custom_class_with_class_argument()
+    {
+        var service = Substitute.For<IMyService>();
+        var argument = new MySampleClassArgument();
+
+        service.MyMethod(argument);
+
+        service.Received().MyMethod(Arg.Any<IMyArgument<SampleClass>>());
+    }
+
+    [Test]
+    public void Supports_matching_generic_interface_bound_type_custom_class_with_derived_class_argument()
+    {
+        var service = Substitute.For<IMyService>();
+        var argument = new MySampleDerivedClassArgument();
+
+        service.MyMethod(argument);
+
+        service.Received().MyMethod(Arg.Any<IMyArgument<SampleClass>>());
+    }
+
+    [Test]
+    public void Supports_matching_custom_class_with_derived_class_argument()
+    {
+        var service = Substitute.For<IMyService>();
+        var argument = new MySampleDerivedClassArgument();
+
+        service.MyMethod(argument);
+
+        service.Received().MyMethod(Arg.Any<MySampleClassArgument>());
+    }
+
+    [Test]
+    public void Supports_matching_generic_interface_bound_type_ArgAnyType_with_class_argument()
+    {
+        var service = Substitute.For<IMyService>();
+        var argument = new MyStringArgument();
+
+        service.MyMethod(argument);
+
+        service.Received().MyMethod(Arg.Any<IMyArgument<Arg.AnyType>>());
+    }
+
+    [Test]
+    public void Supports_matching_generic_interface_bound_type_ArgAnyType_with_derived_class_argument()
+    {
+        var service = Substitute.For<IMyService>();
+        var argument = new MySampleDerivedClassArgument();
+
+        service.MyMethod(argument);
+
+        service.Received().MyMethod(Arg.Any<IMyArgument<Arg.AnyType>>());
+    }
+
+    [Test]
+    public void Does_not_support_matching_ArgAny_of_type_derived_from_base_type_with_string_type_param_to_other_type_derived_from_base_type()
+    {
+        var service = Substitute.For<IMyService>();
+        var argument = new MyOtherStringArgument();
+
+        service.MyMethod(argument);
+
+        service.DidNotReceive().MyMethod(Arg.Any<MyStringArgument>());
+    }
+
+    [Test]
+    public void Does_not_support_matching_ArgAny_of_type_derived_from_base_type_with_custom_type_param_to_other_type_derived_from_base_type()
+    {
+        var service = Substitute.For<IMyService>();
+        var argument = new MyOtherSampleClassArgument();
+
+        service.MyMethod(argument);
+
+        service.DidNotReceive().MyMethod(Arg.Any<MySampleClassArgument>());
+    }
+
     [SetUp]
     public void SetUp()
     {
         _something = Substitute.For<ISomething>();
     }
+
+    public interface IMyService
+    {
+        void MyMethod<T>(IMyArgument<T> argument);
+    }
+    public interface IMyArgument<T> { }
+    public class SampleClass { }
+    public class MyStringArgument : IMyArgument<string> { }
+    public class MyOtherStringArgument : IMyArgument<string> { }
+    public class MySampleClassArgument : IMyArgument<SampleClass> { }
+    public class MyOtherSampleClassArgument : IMyArgument<SampleClass> { }
+    public class MySampleDerivedClassArgument : MySampleClassArgument { }
 }
\ No newline at end of file