A class of models is introduced for the analysis of group differences in the association between two discrete variables. The RC(M) association model for two-way tables is reviewed, and alternative weighting systems for identifying interaction parameters are presented. This model is generalized for the setting where a two-way contingency table is available for two or more groups. Various restricted models can be used to examine possible sources of intergroup heterogeneity in the association. These sources pertain to heterogeneity in the intrinsic association and/or in the scores for the row and column variables. The importance of weights used to identify the row and column scores is emphasized. A classical set of data previously analyzed by many authors is used to illustrate the advantages of the models and methods developed here.