A generalised money demand function (GMDF), based on Box-Cox parametric transformations, has been estimated for Bangladesh. This generalised form reduces to the liner, semi-log and log-linear forms, under certain restrictions. By incorporating different transformations, and by considering equilibrium and disequilibrium versions, the estimates of the generalised money demand function have been compared with those obtained from the restrictive models. A log-likelihood test has been carried out for choosing an appropriate functional form. Our results indicate that the linear form is appropriate for the equilibrium version of the money demand function, while in the disequilibrium version, none of the restricted models seems to be appropriate. The behavioural properties of the alternative models have been examined by considering the movement of income and interest rate elasticities in the sample period. The empirical performance of alternative models in terms of their predictive ability has also been examined. Theil’s U-statistic constructed for this purpose revealed the superiority of estimating the generalised money demand function.