This paper investigates the behaviour of US stock prices using an unrestricted two-regime threshold autoregressive (TAR) model with an autoregressive unit root. The TAR model is applied to monthly stock price (NYSE Common Stocks) data for the US for the period 1964:06 to 2003:04. Amongst our main results, we find that the US stock price is a nonlinear series that is characterized by a unit root process, consistent with the efficient market hypothesis.