The study investigates the stock market efficiency of selected OPEC member countries within the context of random walk hypothesis and volatility approaches using monthly data on stock market indices from January, 2005 to April, 2016. Parametric (variance ratio: homoskedastic and heteroskedastic martingale), nonparametric (the Wright ranks and scores) tests and ARCHtype estimation are performed. Results of both parametric and nonparametric tests indicate that only Qatar's stock market is weak-form efficient. The volatility results suggest that monthly stock returns of OPEC countries are volatile, with Qatar being most volatile and shocks to volatility of stock returns are asymmetric. The implications of this are that: first, investors should be conscious of these shocks when making risk-return decision of their portfolios; second, the results provide useful information to regulators to enable them develop safeguard mechanisms to shield the market from possible asymmetric information emanating from the participants.