Thanks to all who contributed information on history of the notion of a strict n-category. I'd like to summarize for the benefit of those interested what I have learned. The structure of CAT as a strict 2-category was of course implicit in Eilenberg and MacLane's original 1945 definition of categories, functors and natural transformations. Around 1958 Godement observed the significance of what we now call the exchange law relating horizontal and vertical compostion of natural transformations. In 1960 Charles Ehresmann codified our current notion of a strict 2-category and this notion also appeared in the thesis of his student Jean Benabou shortly thereafter. In 1963 Ehresmann published a defintion of n-tuple categories which include strict n-categories as a special case. However, Ehresmann did not isolate strict n-categories themselves as objects worthy of special attention. At the 1965 La Jolla conference Eilenberg and Kelly presented their paper on closed categories which defined strict n-categories recusively as categories enriched in strict n-1 categories. Around the same time the group surrounding Grothendieck at IHES had informally developed a non-recursive definition of strict n-category similar to what is used today. Finally, at the 1969 Bowdin conference, category theorists recognized that the recursive definition of Eilenberg-Kelly and the non recursive definition of the IHES group were equivalent. As far as I can tell the first significant technical development of the theory of strict n-categories (n > 2 ) appeared in a 1981 Cahiers paper by Ronnie Brown and PJ Higgins and in a 1984 Cahiers paper by Dominique Bourn. Carl Futia