A special mechanism of stress relaxation in nanocrystalline films is suggested and theoretically described. The mechanism represents the interfacial sliding accompanied by the formation of wedge disclination dipoles at grain boundaries in nanocrystalline films. The wedge disclination dipoles release, in part, mismatch stresses generated at film-substrate boundaries. It is theoretically shown that the special relaxation mechanism is energetically favorable in various nanocrystalline films deposited onto single crystalline substrates (in particular, AlN/6H-SiC, GaN/6H-SiC, 3C-SiC/Si and Ni/Cu film/substrate systems) in wide ranges of their parameters.