In this paper, we present a parallel version of a multi-objective evolutionary algorithm that incorporates some coevolutionary concepts. Such an algorithm was previosly developed by the authors. Two approaches were adopted to parallelize our algorithm (both of them based on a master-slave scheme): one uses Pthreads (shared memory) and the other one uses MPI (distributed memory). We conduct a small comparative study to analyze the impact that the parallelization has on performance. Our results indicate that both parallel versions produce important improvements in the execution times of the algorithm (with respect to the serial version) while keeping the quality of the results obtained.