Photoluminescence-excitation (PLE) measurements of wide ZnSe/Zn 1 - x Mg x Se single quantum wells (SQW) are presented, performed under high hydrostatic pressure up to 4 GPa. The fully strained samples have been grown by MBE on GaAs(0 0 1) substrates or (1 1 0) substrates. The well transitions 1nH 1 s and 1mL 1 s with n = 1, 2, 3, 4, 5 and m = 1, 2 were recorded as well as excitonic signals from the barrier material at 2 K and their pressure dependence were determined. A cross-over between the: 11L and 13H, as well as between the 12L and 14H transitions, was observed above 1.2 GPa. The transitions were assigned using a modified Kronig Penney model. The exciton binding energy was derived from the energy difference between the 11H 1 s and the 11H 2 s transitions.