In this paper we present a cooperative coevolutive model for the evolution of neural network topology and weights, called MOBNET. MOBNET evolves subcomponents that must be combined in order to form a network, instead of whole networks. The problem of assigning credit to the subcomponents is approached as a multi-objective optimization task. The subcomponents in a cooperative coevolutive model must fulfill different criteria to be useful, these criteria usually conflict with each other. The problem of evaluating the fitness on an individual based on many criteria that must be optimized together can be approached as a multi-criteria optimization problems, so the methods from multi-objective optimization offer the most natural way to solve the problem. In this work we show how using several objectives for every subcomponent and evaluating its fitness as a multi-objective optimization problem, the performance of the model is highly competitive. MOBNET is compared with several standard methods of classification and with other neural network models in solving four real-world problems, and it shows the best overall performance of all classification methods applied. It also produces smaller networks when compared to other models. The basic idea underlying MOBNET is extensible to a more general model of coevolutionary computation, as none of its features are exclusive of neural networks design. There are many applications of cooperative coevolution that could benefit from the multi-objective optimization approach proposed in this paper.