Recent evidence has shown that a subtle alternation in the surface ECG (electrical alternans) may be correlated with the susceptibility to ventricular fibrillation. This paper presents evidence that a mechanical alternation in the heart beat (mechanical alternans) generally accompanies electrical alternans. A simple finite-element computer model, which emulates both the electrical and mechanical activity of the heart, is presented. A pilot animal study is also reported. The computer model and the animal study both found that 1) there exists a regime of combined electrical-mechanical alternans during the transition from a normal rhythm towards a fibrillatory rhythm, 2) the detected degree of alternation is correlated with the relative instability of the rhythm, and 3) the electrical and mechanical alternans may result from a dispersion in local electrical properties leading to a spatial-temporal alternation in the electrical conduction process.