  W. Apel and Yu.A. Bychkov have recently considered the spin relaxation in a
2D quantum Hall system for the filling factor close to unity [PRL v.82, 3324
(1999)]. The authors considered only one spin flip mechanism (direct
spin-phonon coupling) among several possible spin-orbit related ones and came
to the conclusion that the spin relaxation time due to this mechanism is quite
short: around $10^{-10}$ s at B=10 T (for GaAs). This time is much shorter than
the typical time ($10^{-5}$ s) obtained earlier by D. Frenkel while considering
the spin relaxation of 2D electrons in a quantizing magnetic field without the
Coulomb interaction and for the same spin-phonon coupling. I show that the
authors' conclusion about the value of the spin-flip time is wrong and have
deduced the correct time which is by several orders of magnitude longer. I also
discuss the admixture mechanism of the spin-orbit interaction.

Mesoscale and Nanoscale Physics