This study provides strong evidence for the stability of long-run demand functions for narrowly defined money (M1) in five industrial countries (U.S., Japan, Canada, U.K., and West Germany) using post-war quarterly data. Evidence of stability is examined using two different estimation techniques and through a formal test of parameter constancy designed specifically for cointegrating vectors. In the majority of these countries, the key to stability is the imposition of a unitary long-run income elasticity that is rarely rejected by the data.