The main purpose of this paper was to investigate the behaviour and stability of the money multiplier in Tanzania by using un-deseasonalised data for the period 1986:II-2005:I. The results show that short-term interest rates were not significant determinants of the money supply in Tanzania. This finding supports the theory on exogeneity of money supply determination. Even though, both descriptive and regression analyses indicated that the elasticities of the narrow and broad money together with their multipliers were unstable prior to the implementation of market clearing monetary policy regime started in 1993. Moreover, the results attest to existence of a sluggish adjustment of equilibrium money stock to changes in monetary base. This is a typical outcome in economies with nascent financial markets; and, suggests that expansionary monetary policy through open market operations would be inflationary. In general the result suggests that the central bank in Tanzania can, in the due cause, be able to a big extent to control monetary expansion by controlling the base money. Granted, the slight instability in the money multipliers could be controlled for in monetary programming by either accommodating in monetary base or influencing the behaviour of the nonbank sector by other policy measures.