This article examines the martingale difference hypothesis (MDH) and the random walk hypothesis (RWH) for nine conventional and nine Islamic stock indices: Asia-Pacific, Canadian, Developed Country, Emerging, European, Global, Japanese, UK, and United States. It investigates whether Islamic stock indices are more, less, or as efficient as their conventional counterparts. We test four sub-periods of bullish and bearish stock markets, together with the financial meltdown and its recovery, over the period 1997–2012. We use the Escanciano and Lobato’s (2009) automatic portmanteau test (AQ) and Deo’s (2000) test for the MDH. We also apply the automatic variance ratio test (AVR) developed by Choi (1999) and Kim (2009) for the RWH. Over the period from 1997 to 2012, we find that three conventional indices (Europe, Japan, and UK) are efficient, but that none of the Islamic indices are efficient in these markets. During the recent financial crisis, our results indicate slightly more efficiency for the Islamic indices than their conventional counterparts. Our study finds that overall the conventional indices are more efficient than their Islamic counterparts. Nevertheless, during periods of general downturns the Islamic indices have shown the same level of efficiency as their counterparts. Furthermore, it appears that during the last two sub-periods under study, the Islamic indices have moved toward efficiency, displaying the same level of efficiency as their counterparts.