The purpose of this paper is to outline a polynomial approach to modelling and analysing multi-rate control systems. A certain class of system, in which the data input to a digital controller are sampled at a faster rate than the data output, is chosen to illustrate the technique. A set of difference equations defining the propagation of variables during the repetitive time interval engenders a system description whereby the corresponding operations are defined as polynomial functions of the backward-shift operator q(-1). This representation circumvents difficulties associated with the z(N)- transform approach, engendering simple methods of assessing closed-loop stability and assigning poles. Finally, attention is focused upon system performance in the presence of deterministic and stochastic input signals. An example is employed throughout the paper to illustrate developments in the theory.