Labour market assimilation of Danish first generation male immigrants is analysed based on two panel data sets covering the population of immigrants and 10% of the Danish population during 1984-1995. Wages and employment probabilities are estimated jointly in a random effects model which corrects for unobserved cohort and individual effects and panel selectivity due to missing wage information. The results show that immigrants assimilate partially to Danes, but the assimilation process differs between refugees and non-refugees.