Unit root tests, augmented Dickey-Fuller and Phillips-Perron tests, indicate that the bilateral real exchange rates of six small Asian countries (India, Indonesia, Korea, the Philippines, Singapore, and Thailand) and three larger countries (Germany, the U.K., and the U.S.) are not stationary, and each has a unit root over the period January 1973 to December 1989 (i.e., a period of flexible exchange rates). This result does not support purchasing power parity (PPP);The theory of Generalized Purchasing Power Parity (Generalized-PPP) is developed due to the failure of PPP. Generalized-PPP states that the bilateral real exchange rates are, in general, non-stationary since the real fundamental variables are generally non-stationary. If the real fundamental variables of some countries share common trends, these countries' real exchange rates will share the same common trends. By sharing the common trends, these countries' real exchange rates are cointegrated, and there exists at least one stationary linear combination of the real exchange rates. Indeed, PPP is just a special case of Generalized-PPP;Tests for the performance of Generalized-PPP by Johansen's multivariate cointegration methodology are presented. There is evidence in support of Generalized-PPP for the Asian countries as long as the Singapore real exchange rate is included. It is likely that the Singapore real exchange rate is the main linkage for the existence of Generalized-PPP in Asia. On the other hand, Generalized-PPP does hold for each of the small Asian countries (except India) with the three large countries (Germany, the U.K., and the U.S.);The existence of Generalized-PPP implies that there is an error correction model. Using this model, it is possible to use the resulting impulse response functions to trace out the time paths of the various small Asian countries' real exchange rates for shocks in the real exchange rates of larger countries. Both the results of variance decomposition and the impulse response functions indicate that the real exchange rate movements in the small Asian countries are influenced by the shocks in large countries' real exchange rates, especially the largest country, the U.S.