A class of nonlinear additive varyng coefficient models is introduced in this thesis, inspired by ARN model, presented by Mellem, 1997. the coefficients are explicitly modelled. This work is divided in four major parts: a study of most common models in the time series literature; a study of neural networks, focused in backpropagation network; the presentation of the proposed models and the methods used for parameter estimation: and the case studies. Additive models has been the preferencial choice in nonlinear modelling: idea of varyng coefficient and of hybrid models, aren`t news. Hence, the models in the time series literature were analysed, assentialy those closely related with the class of models proposed in this work. Sinse the predominance and constancy in the use of backpropagation network, or its variants, in time series studies and applications, was confirmed by this work, this network was analyzed with more details. This work demonstrated that the proposed models are universal aproximators and could model explicity conditional variance. Moreover, gradient calculus and algorithms for the weight estimation were developed based on the main estimation methods: least mean squares and maximum likelihood. Even though other gradient calculus and otimization algorithms have been sugested, this one was sufficiently adequate for the studied cases. The case studies were divided in two parts: tests with synthetic series and for the nonlinear time series analysts. The obtained results were compared with other models and were superior or, at least, equivalent. Also, these results confirmed that the proposed hybrid model encompass several of the others models