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Very large changes in the Zeeman splittings and in the diamagnetism of excitons as they acquire kinetic energy in wide quantum wells of CdTe are reported. The changes are found to be functions of the translational wave vector Kz of the exciton in the growth direction of the well, irrespective of the width of the well, and are also found to be strong functions of the direction of the magnetic field. The behavior is accounted for by a model in which mixing occurs between the hydrogenic states which describe the exciton in the center of mass or adiabatic approximation. The mixing is ascribed to terms which arise in the Luttinger Hamiltonian when it is extended to describe excitons. Excellent quantitative agreement with experiment, including the results of changing the strain in the wells, is obtained by using Luttinger parameters close to those previously reported. The model is applicable to wide quantum wells made from any zinc-blende semiconductor and confirms that the huge motion induced changes in magnetic properties, observed here for CdTe and previously also for ZnSe and GaAs, should be universal for such materials.