The issue of variable stepsize in the backpropagation training algorithm has been widely investigated and several techniques employing heuristic factors have been suggested to improve training time and reduce convergence to local minima. In this contribution, backpropagation training is based on a modified steepest descent method which allows variable stepsize. It is computationally efficient and posseses interesting convergence properties utilizing estimates of the Lipschitz constant without any additional computational cost. The algorithm has been implemented and tested on several problems and the results have been very satisfactory. Numerical evidence shows that the method is robust with good average performance on many classes of problems. Copyright 1996 Elsevier Science Ltd.