In this paper, one of the methods of using dynamic recurrent neural networks for solving applied problems of control and diagnosing of aircraft engines technical state, including TV3-117, is considered. A method for coding neural networks into signal graphs is proposed, and it is shown that their adjacency matrices can be used as associative memory in step matrix algorithms for solving dynamic recurrent neural networks. It is shown that in fully connected recurrent neural networks, any neuron can be input or output, and one neuron can simultaneously be input and output. Examples of teaching by the evolutionary optimization algorithm for multiextremal problems of recurrent dynamic neural networks intended for control and diagnosing of TV3-117 aircraft engine technical state are given. The functions of activation blocks of neurons in dynamic recurrent neural networks in this work are used difference expressions of simulation models of linear dynamic links. It is shown that for identification in the time domain of transient processes in dynamic systems of the third order, satisfactory accuracy is achieved at the output of any neuron of a recurrent dynamic neural network with four neurons, while it was found that useful information about the dynamic properties of the dynamic system under study can be simultaneously obtained from the output of any neuron network.