This paper considers a matching model of heterogenous workers and jobs which includes onthe- job search. High-educated workers transitorily accept unskilled jobs and continue to search for skilled jobs. We study the implications of this model for the unemployment rates of high and low-educated workers, for the share of mismatched workers and wage inequality both within and between skill groups. The model is used to shed light on the Spanish experience following a large educational upgrading since the mid-eighties.