For them-way contingency table, we consider models that describe the possible multiplicative interactions among themvariables of the table, and we show how to select models that fit the data in the table, using methods that are, in part, somewhat analogous to the usual stepwise procedures in regression analysis. (Themvariables here are dichotomous or, more generally, polytomous variables.) These methods can be applied to build models for any of the following situations: (a) themvariables are response variables and the mutual relationships among the variables are of interest; (b) one of the variables is a response variable and the otherm– 1 variables are factors that may affect the response; (c)m′ of the variables are response variables (1 < m′ <m) and the otherm-m′variables are factors that may affect them′ variables and the mutual relationships among them′ variables. For illustrative purposes, we analyze a 4-way table (actually, a 3 × 23table), considering both linear and quadratic interaction effects.