A significant autocorrelation of returns, also called predictability, may indicate market inefficiency. To test whether market efficiency has improved in transition economies, we develop a methodology based on a time-varying parameter model. We apply this methodology to a set of recently established stock markets over the period April 1994 through June 1999. We find that the Hungarian market always satisfies weak efficiency. For the Czech and Polish markets, we document convergence reward efficiency. On the other hand, a constantly significant level of predictability characterizes the Russian market. For this market, we cannot draw any conclusions concerning market efficiency.