This paper analyzes the long-term dynamics of Chinese stock market prices, using the data series of daily closing spot price indices from Shanghai and Shenzhen stock markets, two major stock exchange markets in China. Both autoregressive and fractional models have been employed: in the former case, we implement standard unit root tests to determine the nonstationarity; while for the fractional I(d) models, we use a parametric testing procedure developed by Robinson (1994) and a semiparametric estimation method based on a ¿local¿ Whittle estimate of d (Robinson, 1995). The results show strong evidence in favour of unit roots and thus lack of mean reverting behaviour for the log-prices series, when using both the classical methods based on integer degrees of differentiation but also when applying fractionally integrated techniques. On the other hand, when examining the volatility processes by means of studying the absolute and the squared returns series, the results strongly support the view of fractional integration in all cases, with the orders of integration fluctuating in the range (0, 0.5). This implies stationary long memory in volatility.