In two-way classification analysis of variance situations there often exists a systematic type of row column interaction. A model is proposed in which the interaction is of the typeQiγiwhereQiis a parameter of theith row, not necessarily associated with the main effect for rows, and γjis the main effect for columnj. The analysis of data according to this model is given, including estimation and tests of significance. The model is more general than that involved in Tukey's “one degree of freedom for non-additivity” and includes the latter as a special case. The relationship between the two methods is discussed. Applications of the method to different types of problems are mentioned and a numerical example is included.