A new mechanism for nucleation of dislocation dipoles at nanoparticles (nanoinclusions) in nanocomposite solids is suggested and theoretically described. The mechanism represents the nucleation of a nanoscale dipole of 'non-crystallographic' partial dislocations whose Burgers vector magnitudes continuously grow during the nucleation process. It is shown that the dislocations nucleated at nanoparticles can be emitted into a matrix in nanocomposites deformed at high mechanical stresses.