The aim of this study is to estimate the demand for real broad (M2) money in Bangladesh using the most recently developed autoregressive distributed lag approach to cointegration analyses. The empirical results show that there is a unique cointegrated and stable long-run relationship among real per capita broad money demand, real per capita income, domestic interest rates and unofficial exchange rate (UM) premiums which act as a surrogate for foreign interest rates. With money as the dependent variable, the results show that the income and interest elasticities are positive while the UM premium elasticity is negative. These results suggest that distortions in the financial and foreign exchange markets should be reduced in order to increase financial saving or monetary accumulation. Our results also reveal that the demand for money in Bangladesh is stable despite the changes in financial and exchange rate policies between 1975 and 1995.