Competitive adjustment processes in labor markets with perfect information but heterogeneous firms and workers are studied. Generalizing results of Shapley and Shubik [7], and of Crawford and Knoer [1], we show that equilibrium in such markets exists and is stable, in spite of workers' discrete choices among jobs, provided that all workers are gross substitutes from each firm's standpoint. We also generalize Gale and Shapley's [3] result that the equilibrium to which the adjustment process converges is biased in favor of agents on the side of the market that makes offers, beyond the class of economies to which it was extended by Crawford and Knoer [1]. Finally, we use our techniques to establish the existence of equilibrium in a wider class of markets, and some sensible comparative statics results about the effects of adding agents to the market are obtained.