In this work we describe a parallel system consisting of feed-forward neural networks supervised by a local genetic algorithm. The system is implemented in a transputer architecture and is used to predict the secondary structures of globular proteins. This method allows a wide search in the parameter space of the neural networks and the determination of their optimal topology for the predictive task. Different neural network topologies are selected by the genetic algorithm on the basis of minimal values of mean square errors on the testing set. When the alpha-helix, beta-strand and random coil motifs of secondary structures are discriminated, the maximal efficiency obtained is 0.62, with correlation coefficients of 0.35, 0.31 and 0.37 respectively. This level of accuracy is similar to that previously attained by means of neural networks without hidden layers and using single protein sequences as input. The results validate the neural network topologies used for the prediction of protein secondary structures and highlight the relevance of the input information in determining the limit of their performance.