The spin response function for electrons confined in a quantum dot is
studied within the time-dependent local spin density approximation (TD
LSDA) of density functional theory. In the long-wavelength regime we p
redict the existence of a low-energy collective dipole (l = 1) spin mo
de. The evolution with electron number of the spin response is studied
and compared with that of the density response. Predictions for the s
tatic dipole polarizability are given.