Extensive development of new neuromorphic element base – non-volatile memory elements based on new physical principles (ReRAM, FRAM etc.) is conducted. These memory elements are used to implement programmable synaptic weights in crossbar architecture, and enable neural network to conduct in-memory computations. However, the sneak currents and leakage currents are a serious limitation on the achievable dimensionality of rows and columns of the crossbar. The features of the implementation of neural networks on memristor crossbars are considered.