In this study, we estimated to what extent monetary quantities such as M3 money overhang (excess money stock), M3 money stock growth, and M3 money stock available in the economy are useful in predicting future inflation in the East African Community (EAC) countries. To investigate this, we used Johansen cointegration analysis to estimate and analyse the stability of the M3 money demand model for each country member of the EAC. From this estimation, we derived a country-specific measure of money overhang. We compared its forecasting power of future inflation with that of money stock growth, and money stock available in the economy. Over the study period (from 2000 to 2012), except for Uganda, we identified a reasonable and stable country-specific M3 money demand model. Also, for predicting future inflation, the estimation results showed that M3 money stock growth is more reliable in Burundi and in Kenya, while M3 money overhang is preferable in Rwanda and M3 money stock in Tanzania.