We consider two models of Hopfield-like associative memory with q-valued neurons: Potts-glass neural network (PGNN) and parametrial neural network (PNN). In these models neurons a n be in more than two different states. The models have the record characteristics of its storage capacity and noise immunity, and significantly exceed the Hopfield model. We present a uniform formalism allowing us to describe both PNN and PGNN. This networks inherent mechanisms, responsible for outstanding recognizing pmperties, are clarified.