The early stages of stress development during epitaxial growth of metal layers with a large misfit in lattice parameters still need in-depth understanding. In this particular study we have focused on Ag-Cu system, which is immiscible and exhibit a large 14% misfit in lattice parameters. Ag/Cu multilayers have been grown by ultrahigh-vacuum evaporation on Si (111) maintained at -20°C, 35°C or 110°C. The thickness of the individual layers is about 100 Å. All the films present the same (111) orientation with a well defined in-plane orientation: <110> Cu or Ag // <110> Si. The stress was monitored during growth with a home-made laser curvature measurement device. The stress vs thickness behaviour is highly asymmetric when comparing Ag/Cu and Cu/Ag. Indeed Ag grown on Cu does not develop any measurable stress at any thickness or temperature, whereas Cu grows on Ag under tensile temperature and thickness-dependent stress. The temperature dependence of this stress relaxation cannot be interpreted with a standard relaxation model including dislocation motion. A possible way to understand the stress temperature dependence is to consider the evolution of microstructure during growth.