This paper addresses flowshop scheduling problems with multiple performance criteria in such a way as to provide the decision maker with approximate Pareto optimal solutions. Genetic algorithms have attracted the attention of researchers in the nineties as a promising technique for solving multi-objective combinatorial optimization problems. We propose a genetic local search algorithm with features such as preservation of dispersion in the population, elitism, and use of a parallel multi-objective local search so as intensify the search in distinct regions. The concept of Pareto dominance is used to assign fitness to the solutions and in the local search procedure. The algorithm is applied to the flowshop scheduling problem for the following two pairs of objectives: (i) makespan and maximum tardiness; (ii) makespan and total tardiness. For instances involving two machines, the algorithm is compared with Branchand-Bound algorithms proposed in the literature. For such instances and larger ones, involving up to 80 jobs and 20 machines, the performance of the algorithm is compared with two multi-objective genetic local search algorithms proposed in the literature. Computational results show that the proposed algorithm yields a reasonable approximation of the Pareto optimal set.