  We study the spin relaxation in an interacting two--dimensional electron gas
in a strong magnetic field for the case that the electron density is close to
filling just one Landau sub--level of one spin projection, i.e., for filling
factor near one. Assuming the relaxation to be caused by scattering with
phonons, we derive the kinetic equations for the electron's spin--density which
replace the Bloch equations in our case. These equations are non--linear and
their solution depends crucially on the filling factor and on the temperature
of the phonon bath. In the limit of zero temperature and for filling factor 1,
the solution relaxes asymptotically with a power law inversely proportional to
time, instead of following the conventional exponential behavior.

Mesoscale and Nanoscale Physics;Strongly Correlated Electrons