Abstract <p>An analysis of modern work in the field of building fast-acting neurons and neural networks was carried out. The algorithm for setting up a multilayer neural network of direct propagation with the activation function of the s-parabola type is presented. The setting was carried out based on the method of reverse error propagation, adapted for the specified new function. Examples of using an s-parabola in artificial neural networks for solving problems of time series recognition and prediction are considered. Recognition was carried out on the example of typical domestic aircraft, where the objects overall dimensions and the invariant moments of their profiles were used as signs. To predict the time series, the readings of one of the small spacecraft sensors were applied. The solutions quality obtained by the proposed approach was compared with solutions based on neural networks with a traditional sigmoid. The s-parabola advantage in terms of learning speed and subsequent solution of the applied problem is shown.</p>