Pairs of bright spots are observed in microphotoluminescence intensity maps of ZnSe/ZnMgSSe quantum-well structures. These pairs are exactly aligned parallel to the [110] or [(1) over bar 10] directions. Atomic-force microscopy and plan-view transmission electron microscopy reveal that the bright emission spots are related to pairs of stacking faults. The enhanced radiative recombination is a result of exciton localization in the region where the stacking faults intersect the quantum wells. Cross-section transmission electron microscopy and microphotoluminescence spectroscopy show that in the case of Frank-type stacking faults (oriented along [110]) the wells are enlarged by up to 12 bilayers. The exciton localization is much shallower in the case of Shockley-type stacking-fault pairs (oriented along [(1) over bar 10]).