In the first two months following a kidney transplant, there are almost invariably rejection episodes, when the patient's body reacts negatively to the presence of the transplanted organ, resulting in a deterioration in functioning of the latter. Clinicians are therefore concerned to find some method of monitoring patients in order to detect sudden changes in the performance of the new kidney. Renal function is indicated by the glomerular filtration rate (GFR), which measures the rate at which various substances are cleared through the kidney, but GFR is not itself directly observable and so clinicians must attempt to infer something about it on the basis of blood or urine concentrations of chemicals for which kidney physiology suggests a simple form of relationship with GFR. This particular study is based on plasma creatinine measurements (Knapp et al., 1977). In a normally functioning kidney, GFR is constant and creatinine is excreted at a constant rate. In a recently transplanted kidney, typically fluctuating between periods of deterioration and improvement in functioning, GFR and plasma creatinine are inversely related. If GFR decreases, the observed concentration of creatinine will increase, and vice versa. In theory, therefore, by monitoring an observed plasma creatinine series for sudden changes it should be possible to infer the occurrence of significant underlying biological changes. In practice, messages in observed plasma creatinine series are obscured by a combination of factors which together add considerable noise to the underlying process. In part, these derive from biological variation and errors arising in the collection, measurement and processing of the data. In addition, however, there is more than one type of abrupt, discontinuous change in pattern which might occur and it is important to be able to distinguish these different forms of change. For this reason, a statistically based, automatic monitoring procedure requires considerable care in modelling the underlying system and observation processes. In particular, it requires the incorporation of substantial prior information based on physiological and clinical expertise. In section 2, we outline the model building process leading to a representation of the evolution of the plasma creatinine series in steady periods (either of improvement or deterioration). This model is extended, in section 3, to incorporate the various forms of discontinuity which may occur in the process. Section 4 summarizes the implementation of the monitoring procedure and section 5 outlines the way in which this procedure is used as a decision aid for clinicians. The emphasis in this paper is on the modelling process. Detailed mathematical developments are given in Smith and West (1983), detailed discussion of the clinical background and