We study the exciton localization in the semimagnetic semiconductor Cd
1-xMnxTe by selective excitation of the exciton photoluminescence. We
show that the energy position of the effective mobility edge for excit
ons is subject to the competition between nonmagnetic and magnetic loc
alization due to the magnetic polaron formation. External magnetic fie
lds affect this competition by suppressing the polaron formation, whic
h shifts the mobility edge.