This paper examines the stock return behaviour in two premier Indian stock markets using Chow-Denning multiple variance ratio and Hinich bicorrelation tests. The former test overcomes size distortion of conventional variance ratio test. The latter test is capable of detecting linear and non-linear dependencies. The study is based on 14 indices relating to the National Stock Exchange (NSE) and Bombay Stock Exchange (BSE), and relates to the period 02/06/1997 to 30/01/2009. The Chow-Denning test rejects the null of random walk for six indices. The Hinich test rejects the null of pure white noise for full sample period. However, the windowed test results of Hinich show that the serial dependencies are not consistent across the sample period for all indices. This indicates presence of episodic dependencies in stock returns surrounded by long periods of pure noise.