Over the past 50 years, much attention has been given to the Prisoner's Dilemma as a metaphor for problems surrounding the evolution and maintenance of cooperative and altruistic behavior. The bulk of this work has dealt with the successfulness and robustness of various strategies. Nowak and May (1992) considered an alternative approach to studying evolutionary games. They assumed that players were distributed across a two-dimensional (2D) lattice, interactions between players occurred locally, rather than at long range as in the well mixed situation. The resulting spatial evolutionary games display dynamics not seen in their well-mixed counterparts. An assumption underlying much of the work on spatial evolutionary games is that the state of all players is updated in unison or in synchrony. Using the framework outlined in Nowak and May (1992), we examine the effect of various asynchronous updating schemes on the dynamics of spatial evolutionary games. There are potential implications for the dynamics of a wide variety of spatially extended systems in biology, physics and chemistry.