The Generalized Extreme Value Model was developed by McFadden for the case with discrete choice sets. The present paper extends this model to cases with both discrete and continuous choice sets and choice sets that are unobservable by the analyst. We also propose behavioral assumptions that justify random utility functions (processes) that have a max-stable structure, i.e., utility processes where the finite-dimensional distributions are of the multivariate extreme value type. Finally we derive nonparametrically testable implications for the choice probabilities in the continuous case.