Efficient retrieval of nested objects is an important issue in advanced database systems. So far, many index methods for nested objects are proposed. However, they do not consider retrieval of nested objects based on the set comparison predicates such as $\supseteq$ and $\subseteq$. In this paper, we propose four set access facilities for nested objects and compare their performance in terms of retrieval cost, storage cost, and update cost. Our analysis shows that a combination of the signature file method and the nested index is very promising for set retrieval of nested objects.