Employing Dutch longitudinal information on 1250 second-generation Moroccan and Turkish migrants we investigate cultural assimilation using attitude questions on marriage and sexuality (including measures of homophobia). Two theoretical approaches guide our analyses. First, it is expected that the family of origin may push migrants in a more conservative direction. Second, it is expected that aspects of individual achievement in social, cultural and socioeconomic domains may pull migrants in more liberal directions. We find that Moroccan and Turkish migrants have considerably more conservative values about marriage and sexuality than natives, but there is also variation within the second generation. Both cross-sectional and longitudinal analyses for migrants indicate that the role of parents is particularly important: migrant children of religiously more orthodox parents and children of parents who were poorly integrated socially and culturally in their youth, currently have more conservative values about marriage and sexuality, even when individual characteristics are controlled for. Of the various aspects of individual achievement, we find that especially social integration of the second generation is a relevant predictor of liberal values, and not socioeconomic indicators of integration. These results remain significant in a stringent longitudinal test which minimises the bias due to reverse causation.