In many circumstances it is useful to know the mean residence time of food substrates within the body following digestion. For instance, such information is crucial to estimate the extent to which dietary components are fermented inside animal stomachs. The mean residence time can be estimated by measuring the rate at which non-absorbable markers, mixed as a supplement into an animals food, are deposited in the animals faeces. The experimental data are analysed with the use of an appropriate mathematical model. We analyse multicompartmental models for the flow of digesta along the gastrointestinal tract of animals. The problem can be treated as a sequence of `tanks' in series. Of interest is the fact that the volume of the tanks is not necessarily constant. For example, following digestion of food, secretion of pancreatic juices may occur; diluting the tracer. Thus the problem can be treated as a series of semi-batch reactors in series. This problem is a good illustration of the application of the methods of chemical reactor engineering to a situation that, at first sight, does not appear to be a chemical engineering problem.