Summary: Two generalizations of the Rasch model are compared: the between-item multidimensional model [R. J. Adams et al., “The multidimensional random coefficients multinomial logit model”, Appl. Psych. Measurement 21, No. 1, 1–23 (1997; doi:10.1177/0146621697211001)], and the mixture Rasch model [R. J. Mislevy and N. Verhelst, “Modeling item responses when different subjects employ different solution strategies”, ibid. 55, No. 2, 195–215 (1990; doi:10.1007/BF02295283); J. Rost, “Rasch models in latent classes: an integration of two approaches to item analysis”, Appl. Psych. Measurement 14, No. 3, 271–282 (1990; doi:10.1177/014662169001400305)]. It is shown that the between-item multidimensional model is formally equivalent with a continuous mixture of Rasch models for which, within each class of the mixture, the item parameters are equal to the item parameters of the multidimensional model up to a shift parameter that is specific for the dimension an item belongs to in the multidimensional model. In a simulation study, the relation between both types of models also holds when the number of classes of the mixture is as small as two. The relation is illustrated with a study on verbal aggression.