Traditional statistical tests of serial independence of stock price changes often show that stock markets are ineffi cient. Our analysis on daily and monthly data confirms this finding for the Croatian and U.S. markets in the 2002-2010 period. However, this result seems to be mainly due to the impact of the crisis of 2008-2009. The observation of monthly data in the pre-crisis period suggests market efficiency in the U.S. and (rather surprisingly) in Croatia also. Daily data indicate a high degree of efficiency of the US stock market before the crisis, but it is impossible to conclude with a satisfying level of confi dence that the Croatian market was inefficient in that period. Furthermore, an elementary moving average crossover trading system beats the CROBEX and S&P 500 indices from 1997 to 2010, indicating market inefficiency. Still, if the same trading rule is applied to the S&P 500 index in an extended time period between 1950 and 2010, the conclusion about market inefficiency becomes less convincing. It seems that (in)efficiency varies both across markets and in the same markets in the long run, but it still remains unknown which processes are the driving factors behind these changes.