The traditional forecasting of events is based on a preliminary design of their models. Employment of such models as a part of the intelligent robots cannot take into account the whole variety of the situations, which may arise. It is desirable that an adequate model of events is formed by a robot itself. In the interests of intellectualization of the autonomous robots the task of predicting events without setting models of their development is considered. Objective is to increase the functionalities of fore-casting of the events with the changing laws of their development. In order to address this problem a new method for predicting is proposed. The method involves the use of a recurrent neural network with controlled synapses and with a layer structure in the form of a double spiral. The method is based on associative memorizing of the current and delayed signals, and extraction of the future events from the memory of the neural network. According to the method is not necessary to know in advance, in accordance with which law the observed events will develop. The development model of such events is formed by the dynamic neural network itself in the process of accumulation of its experience. The method makes it possible to predict the parallel events at various depths with a gradual improvement of the results. These results are the sliding multistep forecasts. Due to this the intelligent robots can qualitatively predict events and plan their responses. The simulation results, reflecting the peculiarities of such prediction, are presented. The recommendations for the use of the proposed method have been formulated.