The partial credit model (PCM) (G. N. Masters, 1982) can be viewed as a generalization of the Rasch model for dichotomous items to the case of polytomous items. In many cases, the PCM is too restrictive to fit the data. Several generalizations of the PCM have been proposed. In this paper, a generalization of the PCM (GPCM), a further generalization of the one-parameter logistic model, is discussed. The model is defined and the conditional maximum likelihood procedure for the method is described. Two statistical tests for the model, based on generalized Pearson statistics, are presented. The first is a generalization of some well-known statistics for the Rasch model for dichotomous items to the GPCM which has power against incorrect specifications of the form of the item characteristic curves. The other test has power against local dependence and multidimensionality, and is built on an approach introduced by A. L. van den Wollenberg (1982) and C. A. W. Glas (1988) for testing unidimensionality in the Rasch model for dichotomous items. Some simulation studies are presented concerning the power of the tests. (Contains 31 references.) (SLD)