We study the multitype contact process on Z(d) under the assumption that one of the types has a birth rate that is larger than that of the other type, and larger than the critical value of the standard contact process. We prove that, if initially present, the stronger type has a positive probability of never going extinct. Conditionally on this event, it takes over a ball of radius growing linearly in time. We also completely characterize the set of stationary distributions of the process and prove a complete convergence theorem. (C) 2018 Elsevier B.V. All rights reserved.