The work is devoted to the problem of nonlinear modeling of objects based on dynamic neural networks. The aim of the work is to improve the accuracy of modeling dynamic objects with significant nonlinearities using neural network models, and identify the scope of their effective application. This aim is achieved by applying the dynamic nonlinear models in the form of time delay neural networks. The scientific novelty of the work lies in the determination of the dependences between the accuracy of suggested models and the types of model input signals, as well as the amplitudes of model input signals. Practical usefulness of the research lies in the determination of the area of effective use of suggested models of dynamic objects with significantly nonlinear features, such us saturation. Significance of the obtained results: the application of the proposed models for identification dynamic objects with significantly nonlinear characteristics allows to improve the accuracy of the modelling process in comparison with models based on deterministic identification methods, such as integro-power series based on multidimensional weight functions.