Artificial neural networks are employed for demodulation of spread-spectrum signals in a multiple-access environment. This paper is motivated in large part by the fact that, in a multiuser system, the conventional (matched filter) receiver suffers sever performance degradation as the relative powers of the interfering signals become large (the "near-far" problem). Furthermore, in many cases the optimum receiver, which alleviates the near-far problem, is too complex to be of practical use. Two simple structures employing multilayer perceptrons are proposed for demodulation of spread-spectrum signals in both synchronous and asynchronous Gaussian channels. The optimum receiver is used to benchmark the performance of the proposed receiver; in particular, it is proven to be instrumental in identifying the decision regions for the neural networks. The neural networks are trained for the demodulation of signals via back-propagation type algorithms. In particular, a modified back-propagation algorithm is introduced for single-user and multiuser detection with near-optimum performance that could have applications in other classification and pattern recognition problems. A comparative performance analysis of the three receivers, optimum, conventional and the one employing neural networks, is carried out via Monte Carlo simulations. An importance sampling technique is employed to reduce the number of simulations necessary to evaluate the performance of these receivers in a multiuser environment. In all examples considered, the proposed neural net receiver significantly outperforms the conventional receiver.