Refectivity spectra taken from wide quantum wells based on CdTe/CdZnTe and GaAs/AlGaAs (in which the well width is much larger than the exciton Bohr radius) were studied in magnetic ¯elds in the plane of the well (the Voigt geometry). The energy splitting between bright and dark excitons and the redistribution of the oscillator strength from bright to dark was observed and this allowed us to determine the exciton exchange constant ¢. We found that exciton translational mass depends on the value of magnetic field. Additionally, we found that diamagnetic shift also depends on exciton wave vector. Changes in the spectra in the range of the overlap of heavy and light hole exciton resonances were observed when the magnetic field was inverted. Theoretical modeling of the spectra allowed us to explain all the observed features in the re°ectivity spectra and to determine some material parameters.