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This paper examines the demand for money under conditions of very high inflation in Argentina, Bolivia, Brazil, Chi le, and Peru during the 1970s and 1980s. The authors test whether the monetary and inflationary experiences of these countries can be adequately characterized by the Cagan (1956) model, using an econometric procedure that is not reliant on any particular assumpti on concerning expectations formation except that forecasting errors are stationary. The authors also examine the importance of foreign asset substitution in domestic portfolios and the hypothesis that monetary policy was tantamount to maximization of the inflation tax revenue before testing the rational expectations hypothesis. Copyright 1993 by MIT Press.