This paper quantifies the effects of increases in military expenditures on education and health spending using local projections and different strategies to identify exogenous changes in military spending based on data for 33 sub-Saharan African (SSA) economies over the period 1990-2023. Specifications with shocks identified through military spending surges and through a fiscal reaction function yield mixed results that typically are neither economically nor statistically significant. But instrumental variables estimates that tackle endogeneity concerns indicate that a one-standard-deviation increase in the share of military spending in total government expenditure reduces the shares of education and health spending by about 1 percentage point over the medium-term. The crowding-out effects tend to materialize sooner for health expenditures, likely because they have a larger discretionary component, while education spending is marked by rigidities. In addition, we find that military spending shocks tend to crowd-out health expenditures when access to international aid is limited, while there is no evidence of crowding-out when aid is relatively amply available. In contrast, it appears that overall debt levels and the state of the business cycle are not significant factors in determining the extent of crowding-out effects of military expenditure.