This study presents theory and some exploratory empirical work on several separate strands of monetarism in an international context and reports the results of tests of the two interrelated hypotheses: (a) the United States' monetary expansion was responsible forthe exportation of inflation to the rest of the world during the period of generally fixed exchange rates that lasted from the end of World War II until August 1971 (followed by the Smithsonian revaluations and generalized floating in March 1973), and (b) foreign nations could not control their money supplies, even in the short run, to prevent importing inflation. Succinctly stated, the monetarist approach to macroeconomic phenomena holds that money is preeminent in determining the short-run shocks to real output and the long-run price level of an economy. However, received theory is simply not clear as to whose money is most important in an international context. Is it the domestic money stock which is kept relativelyindependent of foreign forces under fixed exchange rates through astute central bank policy, at least in the short run? Is it the rest of the world money stock which, under fixed exchange rates, is a close substitute for domestic money? Or is it the money stock of the so-called world's banker, the United States, which drives foreign economies? We address these issues and others in our empirical analysis.