Using international data, this paper explores whether the efficient market hypothesis for real stock prices is supported for different panels. The stationarity of a real stock price has important implications for modeling and forecasting financial activities. On a global scale, we implement the recently developed nonlinear heterogeneous panel unit root test, which allows us to account for possible nonlinearity and cross-section dependence and to identify how many and which countries of the panel contain a unit root. The primary conclusion is that the stationarity of real stock prices varies between regions and levels of economic development. Overall, our empirical results illustrate that real stock prices in these countries are a mixture of stationary (integrated of order zero) and nonstationary (integrated of order one) processes.