Many money demand studies have been carried out on Uganda, however, these studies perceive and incorporate exchange rate as a linear determinant of real money demand. Indeed, exchange rate may have asymmetric effects on real money demand; with exchange rate appreciation having different effects from exchange rate depreciation. Therefore, this is the first study to estimate exchange rate asymmetries in Uganda, for the period 2008Q3 and 2018Q4. The study uses both the linear ARDL and non-linear ARDL methodologies to accomplish its goal. This is also done by incorporating an economic uncertainty index, which is critical, especially in light of the novel global coronavirus pandemic, that has disrupted trade, movement and supply chains. The error correction terms of both models are negative and significant, with the one of the non-linear ARDL twice as much as that of the linear ARDL. Indeed, the study confirms the existence of exchange rate asymmetries on Uganda’s real money demand. In the linear ARDL model, exchange rate has a positive effect in the long run but a negative result in the short run. On one hand, the non-linear ARDL model reveals that an exchange rate depreciation of the Uganda Shillings negatively affects real money demand in the short run. On the other hand, an exchange rate appreciation positively effects real money demand. Notably, economic uncertainty has insignificant effects in both models, except for its lags in the non-linear model. The implication of these findings is that macro-economic policy management in Uganda should be cognizant of these asymmetric effects of exchange rate, for effective planning, policy and implementation.