An estimation of the number of multiplication and addition operations for training artififfcial neural networks by means of consecutive and parallel algorithms on a computer cluster is carried out. The evaluation of the efficiency of these algorithms is developed. The multilayer perceptron, the Volterra network and the cascade-correlation network are used as structures of artififfcial neural networks. Different methods of non-linear programming such as gradient and non-gradient methods are used for the calculation of the weight coefficients.