  We consider the problem of spin relaxation in a two-dimensional electron gas
(2DEG) in a perpendicular magnetic field. We assume that the spin relaxation is
induced by the Rashba spin-orbit (SO) interaction, which appears due to the
inversion asymmetry of the confining potential. Our solution is based on a
microscopic evaluation of the spin density response function of the 2DEG with
impurities and SO interaction. We derive explicit expressions for the
transverse and longitudinal spin relaxation rates. Our analysis shows, in
particular, that the spin relaxation rates exhibit {\it magnetoquantum
oscillations}, which are analogous to the Shubnikov-de Haas oscillations of the
electrical resistivity. These oscillations can be observed, for example, in
time-resolved optical experiments.
