This study aims at examining the efficiency of stock returns of BRICS markets. Here we consider the daily data from 25th September 1997 to 31st March 2018. This study employs variance ratio tests for linear dependencies and BDSL test for nonlinear dependence. Further, the entire period of study is divided into sub-periods such as pre-crisis, crisis and post-crisis periods to understand the level of efficiency in different time periods. The results of variance ratio tests show that Brazil and China markets are weak-form efficient in all time periods while Russia and South Africa are a weak form efficient in the full period, crisis and post-crisis periods but not in pre-crisis period. With regard to Indian stock markets, the markets are found to be weakly efficient during pre-crisis and crisis period while market inefficiency is observed in full period and post-crisis period. However, the results of the nonlinear test show that all the BRICS markets are rejecting the random walk hypothesis due to the nonlinear dependence in all time periods of study.