Perceptron is an artificial neural network that can solve simple tasks such as invariant pattern recognition, linear approximation, prediction and others. We report on the hardware realization of the perceptron with the use of polyaniline-based memristive devices as the analog link weights. An error correction algorithm was used to get the perceptron to learn to implement the NAND and NOR logic functions as examples of linearly separable tasks. The conceptual scheme of two-layer perceptron is proposed to implement all possible logic functions including linearly inseparable ones (as XOR, for example). It is also shown how organic memristive links between two layers of neurons could be made on the base of stochastic block copolymer matrices which greatly simplifies and makes cheaper the mass-production of such networks. The physical realization of a perceptron demonstrates the ability to form the hardware-based neuromorphic networks with the use of organic memristive devices. This holds a great promise towards new approaches for very compact, low-volatile and high-performance neurochips that could be made for a huge number of intellectual products and applications.