This paper characterizes the equilibrium for a large class of search models with two-sided heterogeneity and on-the-job search. Besides the well-known congestion externalities, we show that on-the-job search in combination with monopsonistic wage setting without commitment creates a ' business-stealing' externality. In the absence of congestion effects, this leads to excessive vacancy creation. Under wage setting with commitment this externality is absent because when posting a wage, firms take into account the expected productivity of future workers in their current jobs. If firms are able to make and respond to counteroffers, then they will not have to pay no-quit premia and this also leads to excessive vacancy creation. © 2009 The Review of Economic Studies Limited.