A theoretical model is suggested which describes structural and behavioral features of grain boundary dislocation configurations near triple junctions in nano- and polycrystalline materials. With the elastic interaction between grain boundary dislocations taken into account, we have theoretically examined deviations of spatial arrangement of boundary dislocations near triple junctions, from a periodic arrangement. Also, the local migration of grain boundaries near their triple junctions has been theoretically described, induced by grain boundary sliding in mechanically loaded nano- and polycrystalline materials. In the framework of the model, the key driving force for the local migration is a release of the elastic energy of ensemble of gliding boundary dislocations (carriers of grain boundary sliding) and immobile boundary dislocations (associated with grain boundary misorientation). It is shown that migration is capable of effectively enhancing grain boundary sliding, in which case the combined effects of grain boundary sliding and migration near triple junctions cause plastic flow localization in fine-grained materials, reported in the literature.