On the overspecification of multinomial and nested logit models due to alternative specific constants by M. Bierlaire, T. Lotan and Ph. Toint Report 95/12 October 24th, 1995 Alternative specific constants (ASCs), although playing an important role in random utility models, have received very little attention in theoretical studies. In this paper, we try to fill this gap by providing an analysis of the overspecification caused by ASCs to the log-likelihood function of multinomial and nested logit models. The theoretical results lead directly to a particular strategy of ASC specification, called here the {\em orthogonal strategy}. The analysis of the relationship between any two arbitrary strategies and the derivation of an interesting geometrical property of the orthogonal strategy provide a motivation to prefer the latter.