A semiclassical theory of collective excitations based on the Vlasov equation is applied to the study of surface oscillations in small alkali-metal spheres. It is found that, when due allowance is made for the electron ``spill-out'' and for the exchange-correlation part of the electron-electron interaction, the polarizabilities given by the semiclassical Vlasov theory are similar to those yielded by quantum self-consistent calculations. In particular, the enhancement of the static polarizability and the red shift of the surface-plasmon resonance with respect to the classical values can be reproduced within the present semiclassical approach. Dynamic polarizabilities are evaluated for particles containing from 20 to 2000 sodium atoms.