Many European countries are concerned about the economic integration of low-skilled non-Western migrants. This study investigates skill disparities and their intergenerational persistence by employing a unique combination of Dutch survey and registry data linking math and language skills of parents and their children. We find that skills of non-Western migrants strongly converge towards those of natives; group differences in math and language are reduced by 60 to 70% over one generation. Ethnic externalities that may delay group convergence indefinitely appear not to be important. This suggests that the currently observed skill gaps of non-Western migrants in Europe are unlikely to persist for those migrants.