In this paper, the oscillator strengths of both the heavy-hole and the light-hole excitons in GaAs-AulcornerGaulcornerAs and InulcornerGaulcornerAs-InP quantum wells with the effect of a magnetic field applied along the growth axis are studied. The calculation is carried out usig a variational approach, based on a simple trial exction wave function. The exciton oscillator strengths are found to decrease with increasing well width and to increase with the applied magnetic fields which lead to additional quantum confinement for moderately wide well sizes. Also, the oscillator strengths for the heavy-hole exciton are found to be large than those of the light-hole exciton in these quantum well structures.