This study utilizes tests based on ranks and signs suggested by Wright (2000), in addition to the traditional variance-ratio test, to examine the behavior of United Kingdom real estate and construction security indices. The results suggest a positive dependence in the index return series and provide a strong rejection of the random walk hypothesis for the two U.K. index series examined in this study. Thus, the efficient market hypothesis (EMH) is not confirmed for these real estate securities indices in the U.K.