Based on the requirement of OECD countries to permit substantial inflows of immigrants to compensate for the effects of the demographic change, this paper explores the incentives of heterogeneous migrants to acquire host country specific cultural skills to improve their labor market outcomes. The theoretical results predict that the migrants ambition in achieving such skills is increased if the scope of their respective cultural group is small, social permeability of migrants in the native society is large and individual integration costs are low. Based on these results, I study whether cultural heterogeneity among the migrant population is welfare enhancing for the native population. I find that as long as migrants do not differ too much with regard to their costs of learning the native culture, cultural heterogeneity is beneficial for the host economy. The model provides an explanation for the shift in the immigration policies of the traditional host countries throughout the twentieth century as well as the current immigration policies in the EU member states.