This study applies a complex systems approach to test for the presence of rational bubbles in the Equity REITs market. The applied model is based on theoretical implications of the evolution of prices under rational bubble regimes. The advantage of the approach is twofold. The model is able to detect rational bubbles while they rise and to predict the most likely time of their collapse. We apply the model to daily price data on U.S. Equity REITs from 1989 to 2011. Our findings suggest the existence of a bubble for the period of 2003 to 2007. Tests for sub-markets reveal that the bubble developed in the Residential REITs market, but not in the Office REITs market.