The intersymbol interference problem is one of the major limitations to the transmission of high data rates through a band limited channel (i.e. telephone channel). A channel equalizer is often used in the receiver as a suitable means to treat intersymbol interference. This thesis presents a model of a data transmission system operating at 2400 baud. It then presents the results of computer simulation showing the performance of neural network-based equalizer namely the MultiLayer Perceptron (MLP) and radial basis function (RBF) network. The results show the improvement achieved by neural-based equalizer in tolerance to additive white Gaussian noise over those achieved by the conventional adaptive algorithm. These conventional algorithms include, the zero forcing, minimum mean square error, adaptive least mean square error equalizers and near maximum likelihood detector. The improvement increases as the severity of distortion increases reaching 12dB over the severely distorted telephone channel. Bearing in mind that many conventional algorithms require the estimate of the sampled impulse response of the channel, where as neural based equalizers don't require the estimator. The computer tests where made by software simulation, using MATLAB version 5.1 package running under windows95 and a 4-QAM signal was transmitted over four different practical telephone circuits.