This paper begins with a very simple theoretical question: Do the cultural heritages of the Old World persist among children and grandchildren of the immigrants from the various European countries? Two ethnic groups--the Irish Catholics and the Italians--about whose country of origin there exists something of an anthropological and sociological literature are chosen for study. From this literature are derived a considerable number of hypotheses about their respective differences in the Anglo-Saxon American norm and from one another. To the extent that these hypotheses are sustained by the available evidence, one is able to assert that there is a persistence of diversity of cultural heritage within the United States, predictable on the basis of the culture of the countries of origin. Also, the fact of ethnic cultural diversity in the United States is thereby established, a fact which many social scientists are not yet prepared to concede. An ethnic group is defined here as a large collectivity, based on presumed common origin, which is, at least on occasion, part of a self-definition of a person, and which also acts as a bearer of cultural traits. On the basis of the evidence presented, it can be safely said that it would be very difficult to understand the present behavior of American immigrant groups without knowing something of the cultural heritage from which the groups came. (Author/JM)