We have used the magneto-optical Kerr effect to search for evidence of the oscillatory antiferromagnetic (AF) coupling associated with the recently discovered "Giant Magnetoresistance Effect" (GMR) in Fe/Cu/Fe and Co/Cu/Co multilayers. The GMR effect was reported in samples grown by magnetron sputtering methods on Si wafers. In our work the multilayers are grown by molecular beam epitaxy (MBE) techniques on a Cu(111) single-crystal substrates. None of the resulting multilayers showed any evidence of the oscillatory AF coupling being sought. We have concluded that (111)-oriented crystallites in the sputtered multilayers make little if any contribution to the observed oscillatory AF coupling. However, oscillatory AF coupling does occur in MBE-grown multilayers on Cu(100), and its dependence on Cu thickness is remarkably similar to that of the sputter-deposited multilayers. This suggests that (100)-oriented grains in the sputter-deposited multilayers may be partly, or perhaps even largely, responsible for the AF coupling. Supporting this suggestion are preliminary x-ray diffraction pole-figure measurements we have made on three of the sputter-deposited multilayers which indicate that the tendency to (111) texture is not extremely strong, and that other crystalline grains are present.