Loglinear latent class models are used to detect differential item functioning (DIF). These models are formulated in such a manner that the attribute to be assessed may be continuous, as in a Rasch model, or categorical, as in Latent Class Mastery models. Further, an item may exhibit DIF with respect to a manifest grouping variable, a latent grouping variable, or both. Likelihood-ratio tests for assessing the presence of various types of DIF are described, and these methods are illustrated through the analysis of a "real world" data set