Propositions necessary for development of parallel-hierarchical (PH) network training methods are discussed in this article. Unlike already known structures of the artificial neural network, where non-normalized (absolute) similarity criteria are used for comparison, the suggested structure uses a normalized criterion. Based on the analysis of training rules, a conclusion is made that application of two training methods with a teacher is optimal for PH network training: error correction-based training and memory-based training. Mathematical models of training and a combined method of PH network training for recognition of static and dynamic patterns are developed