  We introduce a multitype contact process with temporal heterogeneity
involving two species competing for space on the $d$-dimensional integer
lattice. Time is divided into seasons called alternately season 1 and season 2.
We prove that there is an open set of the parameters for which both species can
coexist when their dispersal range is large enough. Numerical simulations also
suggest that three species can coexist in the presence of two seasons. This
contrasts with the long-term behavior of the time-homogeneous multitype contact
process for which the species with the higher birth rate outcompetes the other
species when the death rates are equal.
