THE OPTIMAL LEVEL OF domestic money balances may vary according to different degrees of uncertainty concerning the foreign exchange value of the domestic money. That is, in addition to the fundamental determinants of the demand for money-wealth, income, and opportunity cost-certain types of risks, in this case foreign exchange rate uincertainty, may play a role, albeit a small one. In this note, we consider the theoretical arguments supportive of this contention and then present some empirical evidence, based on a variety of money demand functions and using the German economy as the test case. Our findings are strongly suggestive that foreign exchange risk does play a role in determining real money balances.