In this article we test for bubbles in the S&P 500 stock market index using monthly data over the period 1871m1-2004m6. We use fractional integration techniques, allowing for structural breaks and a nonlinear adjustment process of prices to dividends. We find a significant structural break around 1932, a period in which the stock market began rising again after the market crash of 1929. Furthermore, we do not find evidence of asymmetric adjustment of prices to dividends when using both momentum-threshold autoregressive and threshold autoregressive models. Finally, we cannot reject the hypothesis of orders of integration equal to or higher than one and thus, we find support for the existence of bubbles in the S&P 500 stock market index.