  The exciton spin dynamics are investigated both experimentally and
theoretically in two-monolayer-thick GaAs/AlAs quantum wells with an indirect
band gap and a type-II band alignment. The magnetic-field-induced circular
polarization of photoluminescence, $P_c$, is studied as function of the
magnetic field strength and direction as well as sample temperature. The
observed nonmonotonic behaviour of these functions is provided by the interplay
of bright and dark exciton states contributing to the emission. To interpret
the experiment, we have developed a kinetic master equation model which
accounts for the dynamics of the spin states in this exciton quartet, radiative
and nonradiative recombination processes, and redistribution of excitons
between these states as result of spin relaxation. The model offers
quantitative agreement with experiment and allows us to evaluate, for the
studied structure, the heavy-hole $g$ factor, $g_{hh}=+3.5$, and the spin
relaxation times of electron, $\tau_{se} = 33~\mu$s, and hole, $\tau_{sh} =
3~\mu$s, bound in the exciton.
