Structural properties of sputtered Co/Cu and Ni80Fe20/Cu multilayers showing giant magnetoresistance (GMR) have been investigated by methods of X-ray reflectometry and diffraction. The GMR of these multilayers degrades irreversibly after annealing at elevated temperatures. Corresponding changes of interface and lattice properties have been observed. Whereas tendencies of a weak roughness increase in the NiFe/Cu-system. and of a slight demixing in the Co/Cu-system dominate up to 300 degreesC, at higher temperatures significant alterations of the interface structure in NiFe/Cu and of the texture in Co/Cu occur. In both systems, tensile stresses in the layer stack develop after annealing.