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This paper overviews our recent results on the magneto-optics of excitons in wide quantum wells, when the well width is much larger than the exciton Bohr radius. We have demonstrated that the magnetic moment of the exciton increases by an order of magnitude due to its motion along the magnetic field. The effect was observed for a set of quantum well structures with different well widths and based on various semiconductor compounds. The reason for this effect is mixing of the exciton's center-of-mass motion and the internal motion of electron and hole in the exciton.