This paper presents a class of discrete-time models for the study of the control of hospital in-patient admissions. It contends that the use of non-homogeneous Markov chains is appropriate to the problem and allows a wide choice of possibilities to suit many different situations. The restrictions imposed by the Markov property are discussed and methods of generalizing the process are suggested. In particular, the way is opened for models based on a length of stay with Pascal distribution and on scheduling patients with several days' notice.