[en] Orientation of nonspherical cosmic dust grains is found in anisotropic corpuscular or radiative fluxes and in the presence of the magnetic field; cosmic grains being approximated by axially symmetric ellipsoids. A comparatively small twisting of grains is shown to cause differences in scattering right-hand and left-hand circularly polarized photons and growth of the angular momentum. If the period of the grain's angular momentum precession induced by the magnetic field is shorter than the time of orientation by corpuscular or radiative flux, distribution of grains' axes becomes symmetric relative to the magnetic lines. This orientation mechanism easily explains interstellar linear polarization observed in the Galaxy. The mechanisms of grains' orientation near the Becklin-Neugebauer infrared source, in the B 96 reflected cloud near RY Tau and in cometary heads are proposed. (Auth.)