In this paper, we introduce an asynchronous version of the well-known pursuit game. The validity of past results on the synchronous version of the pursuit game is verified in this new setting by considering five kinds of prey: Still prey, randomly moving prey, avoiding prey, linear prey, and linear prey with switching behavior. Genetic programming is used to evolve teams of predators whose capture rates are compared to that of a greedy strategy. Task assignment is used as an explicit means of coordination in the evolved teams of predators. We conclude that evolved teams with explicit coordination outperform greedy non-cooperative strategies when more competent prey is faced.