Abstract
This thesis is concerned with the classical system of differential equations for the competition between two species in which the coefficients of the differential equations are periodic in time. We give conditions for the existence, uniqueness and asymptotic stability of periodic solutions of such systems having both components positive. These conditions generalize the "well-known" conditions for the existence of a stable equilibrium point in the autonomous case. We also consider a model for competition between two species which may be situated in several locations. We give conditions under which the amounts of the species in the various locations tend to become equal with increasing time.