1. The co-ordination of the heart beat with respiration in fish is treated as a problem in coupled oscillators and a mathematical model is developed in terms of the modulation of a sawtoothed waveform by an injected sine wave.

2. It is shown that reducing the coupling between the two oscillators replaces the locked rhythm by various arrhythmias that can be interpreted in terms of the mutual proportions of the periods of the two oscillators and the amplitude of the injected signal.

3. Electrocardiograms from three species of elasmobranch fish, Mustelus antarcticus, Squalus acanthias and Cephaloscyllium isobella are presented and the arrhythmias they show are compared with those generated by the model.

4. It is concluded that the resemblances between the cardiac arrhythmias in fish and in the model suggest that they have their genesis in partial coupling of the cardiac pacemaker with the respiratory rhythm generator.

5. The relation of the fish arrhythmias to the Wenckebach form of A-V block, and to certain variants of the bigeminus rhythm in man is discussed.

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