The paper proposes the ways to apply swarm intelligence strategies to parallelize neuroevolution methods for synthesizing artificial neural networks. The proposed approaches will solve a number of problems that usually arise during designing high-performance computing related to the synthesis of neural networks. The object of research is the process of developing a parallel approach for the neuroevolution synthesis of artificial neural networks, namely, the use of swarm intelligence strategies to solve a number of problems in designing a method that would use the resources of a parallel computer system. One of the most problematic areas is the highly adaptive nature and significant operating time of neuroevolution methods. One way to solve these problems is to use parallel computer systems and distributed computing. However, a number of questions arise when designing a parallel neuroevolution method. During research a number of tasks were solved, which included the analysis and study of neuroevolution methods for synthesizing artificial neural networks and problems of their parallelization. Attention is also paid to swarm intelligence methods, which have gained popularity recently and show good results. The new method developed during the work was based on strategies for organizing work with swarm particles. Thus, sub-populations distributed between threads and individuals were analyzed as individual particles that interact with each other and depend on the local environment. Classical genetic operators were modified by criterion mechanisms to improve adaptability. During the experiments, the developed method was compared with classical methods. During the work, special attention was paid not only to the characteristics of the resulting neuromodels, but also to the load on the processor during Operation. The developed method showed acceptable results for all comparisons. The new approach has significantly improved the quality level of the parallel neuroevolution synthesis method, allowing to evenly use the capabilities of computing nodes in a parallel system.