This paper seeks to establish the relative importance of money and other factors in explaining inflation in Tanzania. The analysis was based on quarterly data for the 1967 – 2005 period. Both long run regression results failed to establish existence of positive one-to-one correspondence between growth rates of three monetary aggregates (M1, M2, M0) and (headline) inflation in Tanzania. The lack of the one-to-one correspondence as predicted by the Quantity Theory of money also emerged form estimated dynamic autoregressive distributed lag (ADL) error correction model (ECM). Instead, other factors, particularly growth in real income, were found to exert the expected depressive influence on inflation. This finding underscores the importance of the demand for money in explaining inflation. Other important structural factors found to influence inflation in Tanzania include nominal exchange rate and inflation inertia. In aggregate the long run influence of changes in money was found to be very small if compared to that exerted by structural factors. This suggests limitations to monetary policy and importance of structural factor in explaining the dynamics of inflation in Tanzania. On account of theoretical controversies and innovations that have characterized inflation theory to-date coupled with methodological issues of interest, more research on inflationary process in Tanzania is called for to anchor or better the results of this paper.