Direct or indirect additivity of production or utility functions implies dependence of substitution effects on income effects. This dependence is eliminated by implicit additivity, or strong separability along isoquants or indifference surfaces. The present study proposes and analyzes two models, with direct an indirect implicit additivity, respectively, which are generally non-homothetic, non-CES, and include less than 3n parameters for n goods. They give rise to log-linear systems of estimable demand relations. Many other models, such as Cobb-Douglas, CES, Direct and Indirect Addilog, CRESH, CDE, and Non-homothetic CES, are simple, testable special cases of either or both of these models.