Full-screen and windowed applications can be minimized by pressing Alt-Tab. The application will continue to run in its minimized state, meaning that the CK_ddEngine's main loop is still running. The only difference is that the engine will no longer blt updates to the screen. An application can check to see if it's minimized by calling CK_ddEngine::isMinimized().
There are difficulties when it comes to minimizing a full-screen application that is running at a pixel depth that is different than the pixel depth of the Windows desktop. When Alt-Tab is pressed the application loses its primary surface. In a full-screen application where the pixel depths match, the library can recover by simply calling the DirectDraw surface's Restore() method. If the pixel depths do not match however, DirectDraw has a bigger problem. In this case the surface was lost because of a mode change, and simply calling Restore() does not work. The DirectDraw objects must be released and re-created.