In 1990s emerging stock markets evolved from small and shallow into sizeable and liquid markets integrated with the world financial system. This paper empirically studies the conjecture that the relationship between market development and efficiency can be possibly captured by the weak-form market efficiency tests applied to moving subsample windows. The variance-ratio-based multiple comparison test (MCT) is applied to weekly and daily returns for 21 emerging stock markets over the 1988-2000 period. For each country, the MCT is used to test for random walk in subsample windows with fixed starting-point and moving end-points as well as those with fixed end-point and moving starting-points. Tests on both weekly and daily return series indicate that over time there is a move toward market efficiency. In those markets that showed rapid development, it becomes difficult to reject the random walk hypothesis as observations pertaining to earlier periods are dropped from the sample. However, in Mexico and the East Asian countries stock price behavior started to diverge from RW behavior soon after the reversal of portfolio equity flows during the financial crises that affected these countries.