The correlation between the giant magnetoresistance Delta R/R, at the first maximum of the oscillating thickness dependence of the magnetoresistance (MR), and the structural and magnetic parameters has been investigated in (Co/Cu) multilayers (ML) deposited by the unusual RF sputtering method. Different textures and interface roughnesses have been induced from magnetic (Fe, Co) and non-magnetic (Cu, Al, Ta, Cr) buffers. The MR is independent of the ML texture and grain size but presents a strong correlation with the interface as deduced from small and large angle XRD and AFM. In high roughness ML the evolution, under increasing applied field, of Delta R/R versus (M/M(s))(2) presents a strong deviation from a standard linear dependence. Such a deviation is attributed to the presence of Co granules in the Cu or/and the buffer matrices when strong interface disorder is induced in the samples. (C) 1999 Published by Elsevier Science B.V. All rights reserved.