The paper presents the efficient training program of multilayer feedforward neural networks. It is based on the best second order optimization algorithms including variable metric and conjugate gradient as well as application of directional minimization in each step. Its efficiency is proved on the standard tests, including parity, dichotomy, logistic and two-spiral problems. The application of the algorithm to the solution of higher dimensionality problems like deconvolution, separation of sources and identification of nonlinear dynamic plant are also given and discussed. It is shown that the appropriately trained neural network can be used for the nonconventional solution of these standard signal processing tasks with satisfactory accuracy. The results of numerical experiments are included and discussed in the paper. Copyright 1996 Elsevier Science Ltd.