This study measures the short-term and long-term contagion effects in U.S. stock markets and REITs (Real Estate Investment Trusts) markets during the periods of subprime mortgage and financial crises. First, we test contagion between the U.S. stock market and the U.S. REITs market. Then, we test the contagion effects between the U.S. REITs market and eighteen international REITs markets, selected from North America, Oceania, Asian and Europe. To catch the asymmetric effect in the volatility structure of index returns and consider the time-varying data, this study employs asymmetric dynamic Copula models that measure contagion effects. The test result in this study shows that the contagion effect exists because of the fact that during the subprime mortgage crisis, the correlation between the U.S. stock market and REITs market significantly increased. Thus, the two markets lost ground together. While managing not to emerge in Asian REITs markets, the contagion then spread from the U.S. REITs market to Canada, Australia and most of the European REITs markets. In the later financial crisis period, however, the number of European REITs markets impacted by contagion from the U.S. REITs market decreased. Except for Singapore, contagion is absent from the Asian REITs markets. Contagion is more obvious in the short term than in the long term. These results imply that the Asian REITs markets are not easily affected by the U.S. REITs market, which in turn implies that investors could obtain the positive effects of international diversification by investing in this portfolio. In addition, investors should reduce the proportion of their investments placed in REITs markets, as well as focus on a long-term diversification strategy.