Stress relaxation in sputtered and annealed Cu0.57Ni0.42Mn0.01 thin films has been studied at various temperatures. The microstructure of the films stabilized by a thermal cycle to 550 °C showed twinned grains of the dimension of the film thickness. Below 200 °C, a small low-temperature high-stress plasticity was observed, probably due to obstacle-controlled dislocation glide. Between 300 and 550 °C distinct plasticity was detected. This can be described by two relaxation processes with exponentially decreasing stress towards a final value. The activation energies for the two processes agree (0.4 eV/atom), the deformation rates differ by a factor of 10. We suppose that (i) the slower process is flow by grain-boundary diffusion limited as a result of the attachment of the film onto the substrate and (ii) the faster process is mechanical twinning with diffusional accommodation at the grain boundaries.