Animal travel speeds have been hypothesized to satisfy several possible optirnality criteria. These include (1) maximize net rate of energy gain (during foraging), (2) minimize energy cost per unit distance, and (3) minimize rate of energy expenditure. These criteria and others have, however, received little justification. General models of animal travel, coupled with the basic hypothesis that travel speeds are such that fitness is maximized, indicate that animals should sometimes behave in accordance with one of the above criteria. These models also indicate that animals should occasionally travel at their maximum sustainable speeds. In general, however, animals would be expected to travel at speeds that satisfy more complicated optimality criteria that include all the various counteracting factors. Hence more information must be available before these predictions can be thoroughly tested. The simplest predictions from the present models arise in the case of travel during foraging. Here the optimal speed, assuming that food affects an animal's fitness by virtue only of its energy content, is the speed that results in the maximum net rate of energy gain. Furthermore, this speed is greater than both the speed for minimum rate of energy expenditure and the speed for minimum cost per unit distance. On the other hand, when travel involves activities other than foraging, the first, but not necessarily the second, of these last two predictions is valid. In the case of foraging, the optimal travel speed increases with increasing body size. This is not necessarily the case, however, for nonforaging activities.