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Additive models have been the preferential choice in nonlinear modeling: parametric or nonparametric, of conditional mean or variance. A new class of nonlinear additive varying coefficient models is presented in this paper. The coefficients are modeled by neural networks (multilayer perceptrons) and, both the conditional mean and conditional variance, are explicitly modeled. The learning algorithm of the neural network is based on a concept of likelihood maximization. Case studies with a nonlinear in variance synthetic series and a non-linear in mean real series are presented.