A biomechanical model of running has been presented. A basic premise has been that the swing time is nearly independent of speed. In fact, both the racehorse and the trotter have nearly equal swing times. Consequently, as speed increases and the stance phase becomes shorter, the horse must compensate by increasing his extension or the length of the airborne phase (or both). The safe speed which allows the horse adequate preparation time for contact of a leg with the ground is calculated, using a stride-by-stride analysis of the motion of the horse. This is seen to be a very sensitive function of the overlap time in the gait. The overlap between the legs appears to affect both the ultimate performance potential of the horse and also his prospects for soundness.