In this paper we analyze the implications for the identification of common stochastic trends among stock price indices of using data transformed on a ?real dollar? basis. By applying a ?general? VAR model where all the relevant variables (stock indices, consumer price indices and the exchange rate) are included, we show that the expected results from the cointegration analysis differ substantially. In particular it is shown that if four common stochastic trends drive the system then cointegration between the indices transformed in nominal dollars should be the relevant test while the use of their ?real dollars equivalent? is superfluous. In cases where three common stochastic trends exist then a reasonable specification of the model would imply that the Purchasing Power Parity condition accounts for one of them while the second one relates to a cointegrating relation between the stock indices in nominal domestic currency terms. We apply the testing methodology developed by Johansen (1992a, 1995a, 1997) and extended by Paruolo (1996) and Rahbek et al. (1999) to examine the presence of I(2) and I(1) components in a multivariate context using monthly data for the US, UK, Germany and Japan for the period 1980 ? 2000. Four possible economic scenarios were considered in a bivariate setting and two of them were found to be statistically supported. By imposing linear restrictions on each cointegrating vector as suggested by Johansen and Juselius (1994), the order and rank conditions for statistical identification are satisfied while the test for economic identification was not significant for each bilateral case, namely US-UK, US-Germany, US-Japan. The main findings suggest that the policy to transform the data into a ?real? dollar basis, which is often encountered in the literature, lacks empirical support. Furthermore, the stability results indicate that cointegration was established in the early 1990s which implies that some form of policy coordination between the G-7 countries was implemented in the aftermath of the October 1987 crisis.