I have received many helpful responses to my question asking who invented n-categories. However, a short while ago I was rereading the 1965 La Jolla paper by Eilenberg and Kelly (Closed categories, Proc. Conf.on Cat. Alg, Springer, 1965). On page 552 of the conference proceedings, chapter 4, section 2 of their paper, the authors write: [S]o one may define an n-category with morphisms of every type i [between 1 and n], a morphism of type i connecting two of type i - 1...". This is a very explicit reference to the notion of a strict n-category. The definition of an n-category given is that of a category enriched in n-1 categories. Eilenberg and Kelly also offer a reference to to Ehresmann's 1963 paper on structured categories but I can only find Ehresman's definition of n-tuple categories in his paper. Carl Futia