Among analysts, technical trading rules are widely used for forecasting security returns. Recent literature provides evidence that these rules may provide positive profits after accounting for transaction costs. This would be contrary to the theory of the efficient market hypothesis which states that security prices cannot be forecasted from their past values or other past variables. This paper uses the daily Dow Jones Industrial Average Index from 1963 to 1988 to examine the linear and nonlinear predictability of stock market returns with simple technical trading rules, by using the nearest neighbors and the feedforward network regressions. Evidence of nonlinear predictability is found in the stock market returns by using the past returns and the buy and sell signals of the moving average rules.