A fast learning algorithm for a multi layer feedforward neural network is proposed in this thesis. The proposed learning algorithm, based on an innovative variable step size and gradient averaging, has excellent properties to overcome major drawbacks of backpropagation algorithm and shows fast convergence speed. Also in this thesis, a new non-linear echo canceller, combined linear-nonlinear transversal filter, using the multi layer perceptron and the linear adaptive filter is proposed. This new echo canceller shows fast convergence speed than other non-linear echo canceller and achieves desired cancellation of echo required for digital data transmission.