diff --git a/src/proto/typval.pro b/src/proto/typval.pro
index b4733fd..f3184d0 100644
--- a/src/proto/typval.pro
+++ b/src/proto/typval.pro
@@ -63,6 +63,8 @@
 int typval_compare_list(typval_T *tv1, typval_T *tv2, exprtype_T type, int ic, int *res);
 int typval_compare_null(typval_T *tv1, typval_T *tv2);
 int typval_compare_blob(typval_T *tv1, typval_T *tv2, exprtype_T type, int *res);
+int typval_compare_class(typval_T *tv1, typval_T *tv2, exprtype_T type, int ic, int *res);
+int typval_compare_object(typval_T *tv1, typval_T *tv2, exprtype_T type, int ic, int *res);
 int typval_compare_dict(typval_T *tv1, typval_T *tv2, exprtype_T type, int ic, int *res);
 int typval_compare_func(typval_T *tv1, typval_T *tv2, exprtype_T type, int ic, int *res);
 int typval_compare_string(typval_T *tv1, typval_T *tv2, exprtype_T type, int ic, int *res);
diff --git a/src/testdir/test_vim9_class.vim b/src/testdir/test_vim9_class.vim
index 8cb9113..b75e58c 100644
--- a/src/testdir/test_vim9_class.vim
+++ b/src/testdir/test_vim9_class.vim
@@ -367,6 +367,50 @@
   v9.CheckScriptFailure(lines, 'E1041:')
 enddef
 
+def Test_class_object_compare()
+  var class_lines =<< trim END
+      vim9script
+      class Item
+        this.nr = 0
+        this.name = 'xx'
+      endclass
+  END
+
+  # used at the script level and in a compiled function
+  var test_lines =<< trim END
+      var i1 = Item.new()
+      assert_equal(i1, i1)
+      assert_true(i1 is i1)
+      var i2 = Item.new()
+      assert_equal(i1, i2)
+      assert_false(i1 is i2)
+      var i3 = Item.new(0, 'xx')
+      assert_equal(i1, i3)
+
+      var io1 = Item.new(1, 'xx')
+      assert_notequal(i1, io1)
+      var io2 = Item.new(0, 'yy')
+      assert_notequal(i1, io2)
+  END
+
+  v9.CheckScriptSuccess(class_lines + test_lines)
+  # TODO: this does not work yet
+  #v9.CheckScriptSuccess(
+  #    class_lines + ['def Test()'] + test_lines + ['enddef', 'Test()'])
+
+  for op in ['>', '>=', '<', '<=', '=~', '!~']
+    var op_lines = [
+          'var i1 = Item.new()',
+          'var i2 = Item.new()',
+          '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:')
+  endfor
+enddef
+
 def Test_class_member()
   # check access rules
   var lines =<< trim END
diff --git a/src/typval.c b/src/typval.c
index 6eae02b..b5d6883 100644
--- a/src/typval.c
+++ b/src/typval.c
@@ -1310,6 +1310,24 @@
 	}
 	n1 = res;
     }
+    else if (tv1->v_type == VAR_CLASS || tv2->v_type == VAR_CLASS)
+    {
+	if (typval_compare_class(tv1, tv2, type, ic, &res) == FAIL)
+	{
+	    clear_tv(tv1);
+	    return FAIL;
+	}
+	n1 = res;
+    }
+    else if (tv1->v_type == VAR_OBJECT || tv2->v_type == VAR_OBJECT)
+    {
+	if (typval_compare_object(tv1, tv2, type, ic, &res) == FAIL)
+	{
+	    clear_tv(tv1);
+	    return FAIL;
+	}
+	n1 = res;
+    }
     else if (tv1->v_type == VAR_DICT || tv2->v_type == VAR_DICT)
     {
 	if (typval_compare_dict(tv1, tv2, type, ic, &res) == FAIL)
@@ -1580,6 +1598,77 @@
 }
 
 /*
+ * Compare "tv1" to "tv2" as classes according to "type".
+ * Put the result, false or true, in "res".
+ * Return FAIL and give an error message when the comparison can't be done.
+ */
+    int
+typval_compare_class(
+	typval_T    *tv1,
+	typval_T    *tv2,
+	exprtype_T  type UNUSED,
+	int	    ic UNUSED,
+	int	    *res)
+{
+    // TODO: use "type"
+    *res = tv1->vval.v_class == tv2->vval.v_class;
+    return OK;
+}
+
+/*
+ * Compare "tv1" to "tv2" as objects according to "type".
+ * Put the result, false or true, in "res".
+ * Return FAIL and give an error message when the comparison can't be done.
+ */
+    int
+typval_compare_object(
+	typval_T    *tv1,
+	typval_T    *tv2,
+	exprtype_T  type,
+	int	    ic,
+	int	    *res)
+{
+    int res_match = type == EXPR_EQUAL || type == EXPR_IS ? TRUE : FALSE;
+
+    if (tv1->vval.v_object == NULL && tv2->vval.v_object == NULL)
+    {
+	*res = res_match;
+	return OK;
+    }
+    if (tv1->vval.v_object == NULL || tv2->vval.v_object == NULL)
+    {
+	*res = !res_match;
+	return OK;
+    }
+
+    class_T *cl1 = tv1->vval.v_object->obj_class;
+    class_T *cl2 = tv2->vval.v_object->obj_class;
+    if (cl1 != cl2 || cl1 == NULL || cl2 == NULL)
+    {
+	*res = !res_match;
+	return OK;
+    }
+
+    object_T *obj1 = tv1->vval.v_object;
+    object_T *obj2 = tv2->vval.v_object;
+    if (type == EXPR_IS || type == EXPR_ISNOT)
+    {
+	*res = obj1 == obj2 ? res_match : !res_match;
+	return OK;
+    }
+
+    for (int i = 0; i < cl1->class_obj_member_count; ++i)
+	if (!tv_equal((typval_T *)(obj1 + 1) + i,
+				 (typval_T *)(obj2 + 1) + i, ic, TRUE))
+	{
+	    *res = !res_match;
+	    return OK;
+	}
+    *res = res_match;
+    return OK;
+}
+
+/*
  * Compare "tv1" to "tv2" as dictionaries according to "type" and "ic".
  * Put the result, false or true, in "res".
  * Return FAIL and give an error message when the comparison can't be done.
@@ -1920,11 +2009,12 @@
 	    return tv1->vval.v_instr == tv2->vval.v_instr;
 
 	case VAR_CLASS:
+	    // A class only exists once, equality is identity.
 	    return tv1->vval.v_class == tv2->vval.v_class;
 
 	case VAR_OBJECT:
-	    // TODO: compare values
-	    return tv1->vval.v_object == tv2->vval.v_object;
+	    (void)typval_compare_object(tv1, tv2, EXPR_EQUAL, ic, &r);
+	    return r;
 
 	case VAR_PARTIAL:
 	    return tv1->vval.v_partial == tv2->vval.v_partial;
diff --git a/src/version.c b/src/version.c
index d257289..2a5b3eb 100644
--- a/src/version.c
+++ b/src/version.c
@@ -696,6 +696,8 @@
 static int included_patches[] =
 {   /* Add new patch number below this line */
 /**/
+    1134,
+/**/
     1133,
 /**/
     1132,
diff --git a/src/vim9.h b/src/vim9.h
index f8e5e56..443eaeb 100644
--- a/src/vim9.h
+++ b/src/vim9.h
@@ -164,6 +164,8 @@
     ISN_COMPAREDICT,
     ISN_COMPAREFUNC,
     ISN_COMPAREANY,
+    ISN_COMPARECLASS,
+    ISN_COMPAREOBJECT,
 
     // expression operations
     ISN_CONCAT,     // concatenate isn_arg.number strings
diff --git a/src/vim9execute.c b/src/vim9execute.c
index 43bae44..a4c6632 100644
--- a/src/vim9execute.c
+++ b/src/vim9execute.c
@@ -4697,6 +4697,8 @@
 	    case ISN_COMPAREFUNC:
 	    case ISN_COMPARESTRING:
 	    case ISN_COMPAREBLOB:
+	    case ISN_COMPARECLASS:
+	    case ISN_COMPAREOBJECT:
 		{
 		    typval_T	*tv1 = STACK_TV_BOT(-2);
 		    typval_T	*tv2 = STACK_TV_BOT(-1);
@@ -4726,10 +4728,19 @@
 			status = typval_compare_string(tv1, tv2,
 							   exprtype, ic, &res);
 		    }
-		    else
+		    else if (iptr->isn_type == ISN_COMPAREBLOB)
 		    {
 			status = typval_compare_blob(tv1, tv2, exprtype, &res);
 		    }
+		    else if (iptr->isn_type == ISN_COMPARECLASS)
+		    {
+			status = typval_compare_class(tv1, tv2, exprtype, &res);
+		    }
+		    else // ISN_COMPAREOBJECT
+		    {
+			status = typval_compare_object(tv1, tv2,
+							       exprtype, &res);
+		    }
 		    --ectx->ec_stack.ga_len;
 		    clear_tv(tv1);
 		    clear_tv(tv2);
@@ -6807,6 +6818,8 @@
 	    case ISN_COMPARELIST:
 	    case ISN_COMPAREDICT:
 	    case ISN_COMPAREFUNC:
+	    case ISN_COMPARECLASS:
+	    case ISN_COMPAREOBJECT:
 	    case ISN_COMPAREANY:
 		   {
 		       char *p;
@@ -6844,6 +6857,9 @@
 			   case ISN_COMPARELIST: type = "COMPARELIST"; break;
 			   case ISN_COMPAREDICT: type = "COMPAREDICT"; break;
 			   case ISN_COMPAREFUNC: type = "COMPAREFUNC"; break;
+			   case ISN_COMPARECLASS: type = "COMPARECLASS"; break;
+			   case ISN_COMPAREOBJECT:
+						 type = "COMPAREOBJECT"; break;
 			   case ISN_COMPAREANY: type = "COMPAREANY"; break;
 			   default: type = "???"; break;
 		       }
diff --git a/src/vim9expr.c b/src/vim9expr.c
index dd938ec..c5897fa 100644
--- a/src/vim9expr.c
+++ b/src/vim9expr.c
@@ -273,7 +273,8 @@
     class_T *cl = (class_T *)type->tt_member;
     if (*name_end == '(')
     {
-	// TODO
+	// TODO: method or function call
+	emsg("compile_class_object_index(): object/class call not handled yet");
     }
     else if (type->tt_type == VAR_OBJECT)
     {
@@ -300,7 +301,7 @@
     else
     {
 	// TODO: class member
-	emsg("compile_class_object_index(): not handled");
+	emsg("compile_class_object_index(): class member not handled yet");
     }
 
     return FAIL;
diff --git a/src/vim9instr.c b/src/vim9instr.c
index f5795cd..bd2c1b4 100644
--- a/src/vim9instr.c
+++ b/src/vim9instr.c
@@ -254,11 +254,11 @@
  */
     int
 generate_add_instr(
-	cctx_T *cctx,
-	vartype_T vartype,
-	type_T *type1,
-	type_T *type2,
-	exprtype_T expr_type)
+	cctx_T	    *cctx,
+	vartype_T   vartype,
+	type_T	    *type1,
+	type_T	    *type2,
+	exprtype_T  expr_type)
 {
     isn_T	*isn = generate_instr_drop(cctx,
 		      vartype == VAR_NUMBER ? ISN_OPNR
@@ -416,6 +416,8 @@
 	    case VAR_LIST: isntype = ISN_COMPARELIST; break;
 	    case VAR_DICT: isntype = ISN_COMPAREDICT; break;
 	    case VAR_FUNC: isntype = ISN_COMPAREFUNC; break;
+	    case VAR_CLASS: isntype = ISN_COMPARECLASS; break;
+	    case VAR_OBJECT: isntype = ISN_COMPAREOBJECT; break;
 	    default: isntype = ISN_COMPAREANY; break;
 	}
     }
@@ -455,6 +457,13 @@
 		exprtype == EXPR_IS ? "is" : "isnot" , vartype_name(vartype1));
 	return ISN_DROP;
     }
+    if (!(exprtype == EXPR_IS || exprtype == EXPR_ISNOT
+		|| exprtype == EXPR_EQUAL || exprtype == EXPR_NEQUAL)
+	    && (isntype == ISN_COMPAREOBJECT || isntype == ISN_COMPARECLASS))
+    {
+	semsg(_(e_invalid_operation_for_str), vartype_name(vartype1));
+	return ISN_DROP;
+    }
     if (isntype == ISN_DROP
 	    || ((exprtype != EXPR_EQUAL && exprtype != EXPR_NEQUAL
 		    && (vartype1 == VAR_BOOL || vartype1 == VAR_SPECIAL
@@ -2512,12 +2521,14 @@
 	case ISN_COMPAREANY:
 	case ISN_COMPAREBLOB:
 	case ISN_COMPAREBOOL:
+	case ISN_COMPARECLASS:
 	case ISN_COMPAREDICT:
 	case ISN_COMPAREFLOAT:
 	case ISN_COMPAREFUNC:
 	case ISN_COMPARELIST:
 	case ISN_COMPARENR:
 	case ISN_COMPARENULL:
+	case ISN_COMPAREOBJECT:
 	case ISN_COMPARESPECIAL:
 	case ISN_COMPARESTRING:
 	case ISN_CONCAT: