We address two fundamental issues associated with the use of cross-nested logit models. On the one hand, we justify the adequate normalization of the model proposed by Wen and Koppelman (2001). On the other hand, we provide an analysis of the correlation structure of the CNL, based on random utility theory. We evaluate the validity of the approximation proposed by Papola (2004), both using theoretical arguments and numerical examples based on the exact formula of the correlation.