We study optimal promotion decisions of hierarchical firms, with one junior and one senior managerial position, which interact in a search and matching labour market. Workers acquire experience over time while being employed in a junior position and the firm has to determine the experience level at which the worker receives a promotion which allows her to fill a senior position. Promoted workers move to the senior position in their current firm, if it is vacant, otherwise they search for senior positions on the market. The promotion cut-offs of the competing firms exhibit strategic complementarity, but we show that generically a unique stable symmetric general equilibrium exists. We find that stronger competition among firms leads to later (earlier) promotions if the initial number of firms is small (large) giving rise to an inverse U-shape relationship. In the presence of two skill groups, stronger competition among firms reduces the importance of skill differences, so the gap in wages and promotion times decreases with the number of firms. The model is compatible with empirical evidence that high-skill workers are promoted faster than the low-skilled and that internal promotions are more frequent than cross-firm moves to a higher hierarchical position.