In multiple-choice items the response probability on an item may be viewed as the result of two distinct latent processes--a cognitive process to solve the problem, and another random process that leads to the choice of a certain alternative (the process of giving the actual response). An incomplete latent class model is formulated that describes the first process by a Rasch model and the second process by a guessing model. Alternative models are specified that contain additional parameters describing differential item functioning (DIF) in the two processes. DIF with respect to either known or unknown subgroups can be tested by a likelihood ratio test that is asymptotically distributed as chi-square. As an example of the model, four five-choice items from the Second International Mathematics Study (1987) with a sample of 3,002 secondary students were considered. A 42-item list of references and 3 data tables are included. (Author/SLD)