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Hybrid semiconductor/molecular (“CMOL”) circuits may be used for hardware implementation of artificial neural network. Our studies show that such networks (“CrossNets”) may eventually exceed the mammal brain in areal density, at much higher speed and acceptable power consumption. In this report, we demonstrate that CrossNets based on simple (two-terminal) molecular devices can work well in at least two modes: as Hopfield networks with high defect tolerance, and multilayer perceptrons.