Abstract The paper analyzes the influence of minimum wages on firms' incentive to train their employees. We show that this influence rests on two countervailing effects: minimum wages (i) augment wage compression and thereby raise firms' incentives to train and (ii) reduce the profitability of employees, raise the firing rate and thereby reduce training. Our analysis shows that the relative strength of these two effects depends on the employees' ability levels. Our striking result is that minimum wages give rise to skills inequality: a rise in the minimum wage leads to less training for low-ability workers and more training for those of higher ability. In short, minimum wages create a ”low-skill trap.” We indicate that this effect may be important empirically. Finally, including workers' incentives to train themselves makes no major difference to our results.