It has been argued that during the 200 years since the French Revolution, its ideals of liberty, equality, and fraternity gradually have become more visible in societies throughout the world. In other words, societies, in one form or another, have tended to walk the path toward the realization of universal ideals; the decline of racial and ethnic prejudice, the acceptance of cultures other than one's own, and the role of the various means of communication in providing fast information about peoples that were once inaccessible are evidence of this point. Therefore, the argument goes, if this continues to be observed, then it is fair to infer that, in about 50 years, the assimilation of all individuals and the full realization of their potential will be possible.This article attempts to discuss the validity of this argument. As its title indicates, it assumes that the acceptance or rejection of assimilationist trends requires the analysis of social variables that may hinder or speed that process such as race, prejudice and discrimination, and class divisions. The article focuses on the social construction of race and its impact on assimilation in the United States and Brazil. These two societies have been chosen not only because they are the ones with which the present writer is most familiar but also because, due to their histories and to the social diversity of their peoples, the issues of race and prejudice play an important role in both.