The main intention of this paper is to investigate, with new daily data, whether prices in the two Chinese stock exchanges (Shanghai and Shenzhen) follow a random-walk process as required by market efficiency. We use two different approaches, the standard variance-ratio test of Lo and MacKinlay (1988) and a model-comparison test that compares the ex post forecasts from a NAÏVE model with those obtained from several alternative models: ARIMA, GARCH and the Artificial Neural Network (ANN). To evaluate ex post forecasts, we utilize several procedures including RMSE, MAE, Theil's U, and encompassing tests. In contrast to the variance-ratio test, results from the model-comparison approach are quite decisive in rejecting the random-walk hypothesis in both Chinese stock markets. Moreover, our results provide strong support for the ANN as a potentially useful device for predicting stock prices in emerging markets.