Neuhauser (1992) considered the competition between two contact processes and showed that on Z2 coexistence is not possible if the death rates are equal and the particles use the same dispersal neighborhood. In this thesis we consider two variations of the competition model. In the first model a species with a long range dispersal kernel competes with a superior competitor with nearest neighbor dispersal. We show that the two species can coexist when we introduce blocks of deaths due to "forest fires". In the second model particles with long range dispersals compete in an environment with two distinct seasons. Birth rate for each species is piecewise constant and periodic. We show that there is coexistence when the two species have distinct growing seasons.
