Interpreting two factor interaction is often difficult, but may sometimes be eased by making use of eovariates associated to each factor. Some linear and non-linear models are considered to this end. In the orthogonal case, the model structure is given by tensor products of vector subspaces. Such a structure naturally applies to main effects. The estimators and their variances'and covariances are given (asymptotic variances in the non-linear case). The choice of a submodel is discussed in the linear case. Finally some remarks are made to generalize these models to models with more than two factors