This work investigates the magnetic and transport properties of Cu-Co thin films with a special reference to their dependence on the film thickness. Such dependencies of the giant magnetoresistance (GMR) effect in silver-based magnetic alloys, such as Ag-Fe, Ag-Co, and Ag-FeNi films, have recently been found, and they were interpreted within the framework of surface spin-flipping scattering. This article reports on similar thickness dependence in the Cu-based alloy, although the spin-orbit interaction in Cu films is much weaker than in Ag films. A reduction of the GMR in the thinnest samples by a factor of 6, compared to the value of as-deposited bulk samples (8.6% in 50 kOe and at 5 K), was accompanied by an increase in resistivity by no more than 50%. A novel vapor-mixing technique of simultaneous sputtering from two sources was used to deposit Cu80Co20 granular thin films of the 20% nominal Co volume fraction. The thickness of the films, ranging from 8 to 400 nm, was measured by the small-angle x-ray reflectivity method. The average size of the Co particles ranging from 2.5 to 3 nm was determined from the superparamagnetic behavior of the Cu-Co granular films. (C) 1999 American Institute of Physics. [S0021-8979(99)18908-4].