Computer simulations of coevolutionary dynamics between two hosts and two parasites show that extensive spatial variation in polymorphism can be maintained among environmentally identical patches. Spatial variation can be maintained under frequent migration when the dynamics within patches are locally unstable, and the cycles in host and parasite abundances remain out of phase among patches. Additionally, spatial variation can be maintained when host-parasite interactions cause local extinctions, and migration subsequently allows for recolonization. The temporal dynamics that cause spatial variation are difficult to study directly because of the long time scale over which they occur. The simulations suggest that sampling over space at one or a few points in time may provide much information about temporal dynamics.