Co-59 NMR, magnetotransport and grazing incidence x-ray scattering studies have been undertaken on a series of Co/Cu(111) multilayers, grown by molecular beam epitaxy (MBE), and subsequently annealed. Magnetotransport measurements showed that the magnetoresistance (Delta rho/rho) decreased only slightly as the annealing temperature was increased, but both the resistivity rho and the change in resistivity Delta rho doubled. NMR measurements showed that the strain in the interior of the Co layers relaxed slightly as a result of annealing while the strain at the interfaces remained constant. A small increase in the ratio of the area under the main NMR line to the area under the interface line, together with a reduction of interface line area, suggests a slight deterioration in the quality of the interfaces as a result of annealing. These observations are consistent with the model that MBE grown multilayers require good quality interfaces for large magnetoresistance (MR). Data from x-ray measurements showed that the increase in resistivity could be explained as a result of alloying between the top Cu layer of the multilayer and the Au capping layer. (C) 1996 American Institute of Physics.