P6new physiological criterion for muscular load sharing is developed. The criterion is based on the assumption that the endurance time of muscular contractions is maximized, hence muscular fatigue is minimized. The optimization problem is cast in the form of a linearly constrained, non-linear MINIMAX optimization. The new method predicts that: (1) there is synergistic muscle action, (2) muscle force increases non-linearly with external force (load), (3) relatively more force is allocated to muscles that have a large maximum force (large muscles), (4) relatively more force is allocated to muscles with a high percentage of slow-twitch fibers (muscles that are fatigue-resistant), (5) the load sharing does not depend on the moment arm of the muscles (although the absolute force levels do depend on this variable). The predicted load sharing between two cat muscles during standing and walking is in good agreement with direct force measurement data from the literature.