A methodology is developed for the statistical modelling of cardiac behaviour and electrocardiograms (ECGs) thai emphasizes (a) the physiological event/detailed waveform hierarchy; and (b) the importance of control and timing in describing the interactions among the several anatomical sub-units of the heart. This methodology has been motivated by a desire to develop improved algorithms for statistical rhythm analysis. Specifically, to develop algorithms that capture cardiac behaviour in a more fundamental way but that stop short of complete accuracy in order to highlight decompositions that can be exploited to simplify statistical inference based on these models. Our models consist of interacting finite-state processes, where a very few of the transition probabilities for each process can take on a small number of different values depending upon the states of neighbouring processes. Each finite-state process is constructed from a very small set of elementary structural elements. We illustrate our methodology by describing models for three cardiac rhythms and include simulation results for one of these, namely the rhyihm known as Wenckebach.