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The random walk hypothesis (RWH) of the velocity of money has often been supported for the developed economies. The literature is, however, far from unanimous. This paper employs the most recent methodological advances in testing for random walks, the multiple variance ratio test, to re-examine the behaviour of the velocity of money in the G-7 countries. Monetary velocity is computed as the ratio of nominal income to contemporaneous money stock, under alternative definitions of income and money. The empirical results from the present study do not support the RWH in most of the G-7 countries, with the US M1 and M2 velocities as exceptions. Furthermore, the results show that the RWH is sensitive to either the definitions of monetary velocity or the sample period of study.