diff --git a/dlls/user32/tests/msg.c b/dlls/user32/tests/msg.c
index f1236cf6e0d..5f10a89ec29 100644
--- a/dlls/user32/tests/msg.c
+++ b/dlls/user32/tests/msg.c
@@ -10440,6 +10440,124 @@ done:
     flush_events();
 }
 
+static void test_PeekMessage3(void)
+{
+    HWND hwnd;
+    BOOL ret;
+    MSG msg;
+
+    hwnd = CreateWindowA("TestWindowClass", "PeekMessage3", WS_OVERLAPPEDWINDOW,
+                         10, 10, 800, 800, NULL, NULL, NULL, NULL);
+    ok(hwnd != NULL, "expected hwnd != NULL\n");
+    flush_events();
+
+    /* GetMessage() and PeekMessage(..., PM_REMOVE) should prefer messages which
+     * were already seen. */
+
+    SetTimer(hwnd, 1, 0, NULL);
+    while (!PeekMessageA(&msg, NULL, 0, 0, PM_NOREMOVE));
+    ok(msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    PostMessageA(hwnd, WM_USER, 0, 0);
+    ret = PeekMessageA(&msg, NULL, 0, 0, PM_NOREMOVE);
+    todo_wine
+    ok(ret && msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    todo_wine
+    ok(ret && msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    todo_wine
+    ok(ret && msg.message == WM_USER, "msg.message = %u instead of WM_USER\n", msg.message);
+    ret = PeekMessageA(&msg, NULL, 0, 0, 0);
+    ok(!ret, "expected PeekMessage to return FALSE, got %u\n", ret);
+
+    SetTimer(hwnd, 1, 0, NULL);
+    while (!PeekMessageA(&msg, NULL, 0, 0, PM_NOREMOVE));
+    ok(msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    PostMessageA(hwnd, WM_USER, 0, 0);
+    ret = PeekMessageA(&msg, NULL, 0, 0, PM_REMOVE);
+    todo_wine
+    ok(ret && msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = PeekMessageA(&msg, NULL, 0, 0, PM_REMOVE);
+    todo_wine
+    ok(ret && msg.message == WM_USER, "msg.message = %u instead of WM_USER\n", msg.message);
+    ret = PeekMessageA(&msg, NULL, 0, 0, 0);
+    ok(!ret, "expected PeekMessage to return FALSE, got %u\n", ret);
+
+    /* It doesn't matter if a message range is specified or not. */
+
+    SetTimer(hwnd, 1, 0, NULL);
+    while (!PeekMessageA(&msg, NULL, WM_TIMER, WM_TIMER, PM_NOREMOVE));
+    ok(msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    PostMessageA(hwnd, WM_USER, 0, 0);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    todo_wine
+    ok(ret && msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    todo_wine
+    ok(ret && msg.message == WM_USER, "msg.message = %u instead of WM_USER\n", msg.message);
+    ret = PeekMessageA(&msg, NULL, 0, 0, 0);
+    ok(!ret, "expected PeekMessage to return FALSE, got %u\n", ret);
+
+    /* But not if the post messages were added before the PeekMessage() call. */
+
+    PostMessageA(hwnd, WM_USER, 0, 0);
+    SetTimer(hwnd, 1, 0, NULL);
+    while (!PeekMessageA(&msg, NULL, WM_TIMER, WM_TIMER, PM_NOREMOVE));
+    ok(msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    ok(ret && msg.message == WM_USER, "msg.message = %u instead of WM_USER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    ok(ret && msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = PeekMessageA(&msg, NULL, 0, 0, 0);
+    ok(!ret, "expected PeekMessage to return FALSE, got %u\n", ret);
+
+    /* More complicated test with multiple messages. */
+
+    PostMessageA(hwnd, WM_USER, 0, 0);
+    SetTimer(hwnd, 1, 0, NULL);
+    while (!PeekMessageA(&msg, NULL, WM_TIMER, WM_TIMER, PM_NOREMOVE));
+    ok(msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    PostMessageA(hwnd, WM_USER + 1, 0, 0);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    ok(ret && msg.message == WM_USER, "msg.message = %u instead of WM_USER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    todo_wine
+    ok(ret && msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    todo_wine
+    ok(ret && msg.message == WM_USER + 1, "msg.message = %u instead of WM_USER + 1\n", msg.message);
+    ret = PeekMessageA(&msg, NULL, 0, 0, 0);
+    ok(!ret, "expected PeekMessage to return FALSE, got %u\n", ret);
+
+    /* Also works for posted messages, but the situation is a bit different,
+     * because both messages are in the same queue. */
+
+    PostMessageA(hwnd, WM_TIMER, 0, 0);
+    while (!PeekMessageA(&msg, NULL, WM_TIMER, WM_TIMER, PM_NOREMOVE));
+    ok(msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    PostMessageA(hwnd, WM_USER, 0, 0);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    ok(ret && msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    ok(ret && msg.message == WM_USER, "msg.message = %u instead of WM_USER\n", msg.message);
+    ret = PeekMessageA(&msg, NULL, 0, 0, 0);
+    ok(!ret, "expected PeekMessage to return FALSE, got %u\n", ret);
+
+    PostMessageA(hwnd, WM_USER, 0, 0);
+    PostMessageA(hwnd, WM_TIMER, 0, 0);
+    while (!PeekMessageA(&msg, NULL, WM_TIMER, WM_TIMER, PM_NOREMOVE));
+    ok(msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    ok(ret && msg.message == WM_USER, "msg.message = %u instead of WM_USER\n", msg.message);
+    ret = GetMessageA(&msg, NULL, 0, 0);
+    ok(ret && msg.message == WM_TIMER, "msg.message = %u instead of WM_TIMER\n", msg.message);
+    ret = PeekMessageA(&msg, NULL, 0, 0, 0);
+    ok(!ret, "expected PeekMessage to return FALSE, got %u\n", ret);
+
+    DestroyWindow(hwnd);
+    flush_events();
+}
+
 static INT_PTR CALLBACK wm_quit_dlg_proc(HWND hwnd, UINT message, WPARAM wp, LPARAM lp)
 {
     struct recvd_message msg;
@@ -14563,6 +14681,7 @@ START_TEST(msg)
     test_ShowWindow();
     test_PeekMessage();
     test_PeekMessage2();
+    test_PeekMessage3();
     test_WaitForInputIdle( test_argv[0] );
     test_scrollwindowex();
     test_messages();