This paper proposes a concept of a new approach to the development of speech recognition systems using multi-agent neurocognitive modeling. The fundamental foundations of these developments are based on the theory of cognitive psychology and neuroscience, and advances in computer science. The purpose of this work is the development of general theoretical principles of sound image recognition by an intelligent robot and, as the sequence, the development of a universal system of automatic speech recognition, resistant to speech variability, not only with respect to the individual characteristics of the speaker, but also with respect to the diversity of accents. Based on the analysis of experimental data obtained from behavioral studies, as well as theoretical model ideas about the mechanisms of speech recognition from the point of view of psycholinguistic knowledge, an algorithm resistant to variety of accents for machine learning with imitation of the formation of a person’s phonemic hearing has been developed.