Computational neural networks have recently been used to predict the mapping between protein sequence and secondary structure. They have proven adequate for determining the first-order dependence between these two sets, but have, until now, been unable to garner higher-order information that helps determine secondary structure. By adding neural network units that detect periodicities in the input sequence, we have modestly increased the secondary structure prediction accuracy. The use of tertiary structural class causes a marked increase in accuracy. The best case prediction was 79% for the class of all-alpha proteins. A scheme for employing neural networks to validate and refine structural hypotheses is proposed. The operational difficulties of applying a learning algorithm to a dataset where sequence heterogeneity is under-represented and where local and global effects are inadequately partitioned are discussed.