There has been a growing awareness in recent years of the need for health administrators to consider the objectives and welfare of both patients and staff when formulating working policy, and, in particular, the widespread introduction of appoint ment schemes in a wide range of clinics and general practice surgeries has been an important instrument in balancing the time wasted by doctors (in waiting for patients to arrive) and patients (in a queueing system). This paper considers some computer simulations of such appointment schemes and describes some aspects of the queueing systems that they represent, with particular reference to radi ology departments.