This research attempts to evaluate the stability of money demand functions and estimate monetary inflation models in the East African Community (EAC), using quarterly aggregate data that range from 2000Q1 to 2012Q3. We used Johansen co-integration 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. Regarding country-specific money demand functions, with the exception of 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. As both country-specific and regional (EAC area) information on monetary quantity growth and its impact on price level is important to know in a monetary union, we considered the EAC area as a single market and attempted to estimate the aggregate (EAC area) demand functions for broad money M2 and M3 using Johansen co-integration analysis. The estimated long-run aggregate money demand models M2 and M3 appeared to be stable over the sample period. However, the aggregate M2 and M3 at the EAC level were proven to be weakly exogenous, which should discard them for consideration at the EAC level as the intermediate targets variables in order to achieve the overall objective of price stability in the EAC region. Instead, short-term interest rate should be given a prominent role in monetary policy framework at the EAC level.