The steady-state circular-polarized photoluminescence in semimagnetic asymmetric double quantum wells based on Cd(Mn,Mg)Te is studied thoroughly in relation to the polarization of intrawell nonresonance photoexcitation in magnetic fields Bup to 9 T. In low fields B, in which the exciton in the magnetic well is higher in energy than the exciton in the nonmagnetic well, the complete interwell relaxation of excitons is observed. In fields higher than B c = 3-6 T, at which the exciton level in the magnetic well crosses the field-independent exciton level in the nonmagnetic well, the magnetic-field-induced red shift of the exciton in the magnetic well is accompanied by the establishment of a nonequilibrium distribution of excitons. This suggests that spin relaxation plays an important part in the interwell separation of excitons in the spin-dependent potential of the heterostructure. The efficiency of spin relaxation is controlled by mixing of valence band states in the nonmagnetic well and by splitting of heavy and light holes Δ hh-lh . Different modes of interwell tunneling are observed in different field regions separated by the field B c * > B c corresponding to the crossing of the localized excitons in the nonmagnetic well and free excitons in the magnetic well. Possible mechanisms of interwell tunnel relaxation are discussed.