The purpose of this paper is to test the long-term dependence in the Indian stock market returns. The study apply the variance ratio tests under the hypotheses of homoscedasticity as well as heteroscedasticity, and use the data both at the aggregate level of market indices and disaggregate level of individual stocks. The results show statistically significant short-run dependencies, but there is no evidence of departures from random walk in the very long-run . When we used the modified test procedures of Lo and MacKinlay (1988) and Chow and Denning (1993), the evidence was stronger against rejecting the random walk hypothesis in the long-run. However, at disaggregated level of individual stocks, the dependence was stronger compared to the aggregate level.