A large class of random utility models can be expressed in terms of multivariate (dependent) Weibull distributions. This class includes Luce's choice model, McFadden's generalized extreme value class, and Tversky's elimination by aspects model. A major advantage of this class is that one can obtain simple closed form representations of the predicted choice probabilities and reaction times. In this paper I develop a ‘process’ model that gives a natural interpretation of the origins of these models, and discuss various limitations, and possible extensions, of such mod