diff --git a/src/testdir/test_vim9_class.vim b/src/testdir/test_vim9_class.vim
index b75e58c..81076f8 100644
--- a/src/testdir/test_vim9_class.vim
+++ b/src/testdir/test_vim9_class.vim
@@ -394,9 +394,8 @@
   END
 
   v9.CheckScriptSuccess(class_lines + test_lines)
-  # TODO: this does not work yet
-  #v9.CheckScriptSuccess(
-  #    class_lines + ['def Test()'] + test_lines + ['enddef', 'Test()'])
+  v9.CheckScriptSuccess(
+      class_lines + ['def Test()'] + test_lines + ['enddef', 'Test()'])
 
   for op in ['>', '>=', '<', '<=', '=~', '!~']
     var op_lines = [
@@ -405,9 +404,8 @@
           'echo i1 ' .. op .. ' i2',
           ]
     v9.CheckScriptFailure(class_lines + op_lines, 'E1153: Invalid operation for object')
-    # TODO: this does not work yet
-    #v9.CheckScriptFailure(class_lines
-    #      + ['def Test()'] + op_lines + ['enddef', 'Test()'], 'E99:')
+    v9.CheckScriptFailure(class_lines
+          + ['def Test()'] + op_lines + ['enddef', 'Test()'], 'E1153: Invalid operation for object')
   endfor
 enddef
 
diff --git a/src/version.c b/src/version.c
index 4855121..9e06cd4 100644
--- a/src/version.c
+++ b/src/version.c
@@ -696,6 +696,8 @@
 static int included_patches[] =
 {   /* Add new patch number below this line */
 /**/
+    1139,
+/**/
     1138,
 /**/
     1137,
diff --git a/src/vim9expr.c b/src/vim9expr.c
index c5897fa..5a6b110 100644
--- a/src/vim9expr.c
+++ b/src/vim9expr.c
@@ -273,8 +273,47 @@
     class_T *cl = (class_T *)type->tt_member;
     if (*name_end == '(')
     {
-	// TODO: method or function call
-	emsg("compile_class_object_index(): object/class call not handled yet");
+	if (type->tt_type == VAR_CLASS)
+	{
+	    garray_T	*instr = &cctx->ctx_instr;
+	    if (instr->ga_len > 0)
+	    {
+		isn_T *isn = ((isn_T *)instr->ga_data) + instr->ga_len - 1;
+		if (isn->isn_type == ISN_LOADSCRIPT)
+		{
+		    // The class was recognized as a script item.  We only need
+		    // to know what class it is, drop the instruction.
+		    --instr->ga_len;
+		    vim_free(isn->isn_arg.script.scriptref);
+		}
+	    }
+
+	    for (int i = 0; i < cl->class_class_function_count; ++i)
+	    {
+		ufunc_T *fp = cl->class_class_functions[i];
+		// Use a separate pointer to avoid that ASAN complains about
+		// uf_name[] only being 4 characters.
+		char_u *ufname = (char_u *)fp->uf_name;
+		if (STRNCMP(name, ufname, len) == 0 && ufname[len] == NUL)
+		{
+		    *arg = skipwhite(name_end + 1);
+		    int		argcount = 0;
+		    if (compile_arguments(arg, cctx, &argcount,
+						       CA_NOT_SPECIAL) == FAIL)
+			return FAIL;
+		    return generate_CALL(cctx, fp, argcount);
+		}
+	    }
+
+	    semsg(_(e_method_not_found_on_class_str_str),
+							 cl->class_name, name);
+	    return FAIL;
+	}
+	else
+	{
+	    // TODO: method call
+	    emsg("compile_class_object_index(): object call not handled yet");
+	}
     }
     else if (type->tt_type == VAR_OBJECT)
     {
diff --git a/src/vim9type.c b/src/vim9type.c
index 8ce5948..c85c3f6 100644
--- a/src/vim9type.c
+++ b/src/vim9type.c
@@ -581,6 +581,11 @@
 	}
     }
 
+    if (tv->v_type == VAR_CLASS)
+	member_type = (type_T *)tv->vval.v_class;
+    else if (tv->v_type == VAR_OBJECT && tv->vval.v_object != NULL)
+	member_type = (type_T *)tv->vval.v_object->obj_class;
+
     type = get_type_ptr(type_gap);
     if (type == NULL)
 	return NULL;