  We study the spin relaxation (SR) of a two-dimensional electron gas (2DEG) in
the quantized Hall regime and discuss the role of spatial inhomogeneity effects
on the relaxation. The results are obtained for small filling factors ($\nu\ll
1$) or when the filling factor is close to an integer. In either case SR times
are essentially determined by a smooth random potential. For small $\nu$ we
predict a "magneto-confinement" resonance manifested in the enhancement of the
SR rate when the Zeeman energy is close to the spacing of confinement sublevels
in the low-energy wing of the disorder-broadened Landau level. In the resonant
region the $B$-dependence of the SR time has a peculiar non-monotonic shape. If
$\nu\simeq 2n+1$, the SR is going non-exponentially. Under typical conditions
the calculated SR times range from $10^{-8}$ to $10^{-6} $s.
