SYNOPSIS: Most mammals use symmetrical gaits (such as the trot) at moderate speeds but change to asymmetrical gaits (gallops) at high speeds. A mathematical model of quadrupedal gaits failed to show any advantage in this change: it seemed to show that, even at high speeds, there was always a symmetrical gait that was at least as economical as galloping. That model treated the back as rigid, but another model seemed to show that back movements such as occur in galloping could only increase the energy cost. However, metabolic measurements on horses showed that galloping is more economical than trotting at high speeds. The explanation seems to be that kinetic energy fluctuations, due to backward and forward swinging of the legs, become very large at high speeds. Galloping makes it possible for kinetic energy associated with leg movements to be stored briefly as strain energy in elastic structures in the back, and returned in an elastic recoil. The most important of the strain energy stores in the back, that have been discovered so far, is the aponeurosis of the longissimus muscle.