1. The time course of build-up or decline of twitch tension in response to enhancement or reduction of the external calcium concentration was determined in frog heart ventricles, in the hypodynamic state as well as under non-hypodynamic conditions.2. The tension build-up induced by high calcium was greatly slowed when the heart passed into the hypodynamic state, whereas the decline in low calcium was little altered by this condition.3. The tension decline consisted of two approximately exponential phases, an initial rapid phase (t((1/2)) between 3 and 10 sec) and a later slow phase (t((1/2)) between 50 and 180 sec).4. A similar composite time course of tension build-up only occurred under certain conditions: (a) in ventricles in which the hypodynamic state had not developed; (b) after a conditioning period of exposure to enhanced calcium or reduced sodium concentrations.5. The results are explained on the assumption that contraction is brought about by the co-operative action inside heart cells of two calcium compounds whose concentrations change at different rates after variation of the external calcium concentration.6. Formal relationships describing the dependence of twitch tension on the concentration of these two hypothetical compounds are obtained.A tentative explanation of the development of the hypodynamic state is also proposed.