The work is devoted to the development of the radial basis functions (RBF networks) neural network new architecture – a polymorphic RBF network in which the one-dimensional radial basis functions (RBFs) in the hidden layer instead, multidimensional RBFs are used, which makes it possible to better approximate complex functions that depend on several independent variables. Moreover, in its second layer, the summing the RBF outputs one by one from each group instead, multiplication is used, which allows the polymorphic RBF network to better identify relations between independent variables. Based on the training classical RBF networks evolutionary algorithm, the polymorphic RBF network training algorithm was created, which, through the initializing weight coefficients methods use taking into account the tasks structure and preliminary values, using the mutations tournament selection, adding additional criteria to the fitness function to take into account stability and speed training a polymorphic RBF network, as well as using an evolutionary mutation strategy, allowed us to obtain the lowest errors in training and testing a polymorphic RBF network compared to known RBF network architectures. The created polymorphic RBF network practical application possibility is demonstrated experimentally using the helicopters turboshaft engines (using the example, the TV3-117 turboshaft engine) operating process parameters optimizing solving task using a multicriteria optimization algorithm. The optimal Pareto front was obtained, which made it possible to obtain the engine operation three additional modes: maximum reduction of specific fuel consumption at the total pressure in the compressor increase degree increased value by 5.0 %, specific fuel consumption minimization at the total pressure in the compressor increase degree reduced value by 1.0 %, the total pressure in the compressor increases degree optimal value with a slight increase in specific fuel consumption by 10.5 %. Future research prospects include adapting the developed methods and models into the general concept for monitoring and controlling helicopter turboshaft engines during flight operations. This concept is implemented in the neural network expert system and the on-board automatic control system.