The effect of adding blends of linear low-density polyethylene (LLDPE) and ethylene-octene copolymer (EOC) functionalized by grafting (in the course of reactive extrusion) of trans-ethylene-1,2-dicarboxylic acid (TEDA) onto polyamide 6 (PA6) and polyamide 66 (PA66) on rheological and elastic properties of their melts, structural morphology, and mechanical properties has been studied. It is shown that PA66/functionalized polyolefins (fPO) blends are characterized by more significant changes in the characteristics being analyzed as compared to PA6/fPO blends. A phenomenally sharp increase (by more than two decimal orders of magnitudes) in the melt viscosity of PA66/fPO blend as compared to the initial PA66 was established. At the same time, the melt strength may increase more than 50-fold. The degree of TEDA grafting (beta) onto PO macromolecules is the most important parameter determining the level of the values of property indices, as well as the structural features of PA/fPO blends. Only when particular beta values (varying in a relatively narrow range) are reached, a quasi-homogeneous morphology is formed in PA/fPO blends and their deformation capacity as well as the impact strength of materials increase dramatically. The observed effects are caused by the influence of TEDA grafting on interphase interactions in PA/fPO and PA66/fPO blends.