This paper proposes a neural network approach for forecasting short-term electricity prices. Almost until the end of last century, electricity supply was considered a public service and any price forecasting which was undertaken tended to be over the longer term, concerning future fuel prices and technical improvements. Nowadays, short-term forecasts have become increasingly important since the rise of the competitive electricity markets. In this new competitive framework, short-term price forecasting is required by producers and consumers to derive their bidding strategies to the electricity market. Accurate forecasting tools are essential for producers to maximize their profits, avowing profit losses over the misjudgement of future price movements, and for consumers to maximize their utilities. A three-layered feedforward neural network, trained by the Levenberg-Marquardt algorithm, is used for forecasting next-week electricity prices. We evaluate the accuracy of the price forecasting attained with the proposed neural network approach, reporting the results from the electricity markets of mainland Spain and California.