—— Hybrid semiconductor/nanodevice (“CMOL”) technology may allow the implementation of digital and mixed-signal integrated circuits, including artificial neural networks (“CrossNets”), with unparalleled density and speed. However, previously suggested methods of CrossNet training may be impracticable for large-scale applications of these networks. In this work, we are describing two new methods of “in situ” training of CrossNets, based on either genuinely stochastic or pseudo-stochastic multiplication of analog signals, which may be readily implemented in CMOL circuits. The methods have been tested by numerical simulation of CrossNet-based perceptrons by error backpropagation on three problems of the Proben1 benchmark dataset. The testing gave very encouraging results: CMOL CrossNets with their binary elementary synapses may provide, after the in situ training, classification performance at least on a par with the best results reported for software-based networks with c...