The unpyrolyzed non-precious metal-polymer nanocomposite electrocatalysts for the oxygen reduction reaction (ORR) based on amino-substituted analogues of polyaniline (poly-o-phenylenediamine—PoPDA, poly-m-phenylenediamine—PmPDA), cobalt and carbon black were obtained. Composition, morphology, structure and electrochemical properties of nanocomposite electrocatalysts were characterized by C,H,N-analysis, atomic absorption spectrometry, scanning electron microscopy, powder X-ray diffraction, FTIR spectroscopy and cyclic voltammetry. It was shown that differences in the structure of PoPDA and PmPDA caused by the position of the amino groups in the aromatic ring of the starting monomers, as well as conditions for their preparation, are responsible for the difference in the electrochemical properties of hybrid composites based on such polymers. It was found that nanocomposite electrocatalysts based on PmPDA (ORR onset potential, E onset up to 530 mV; ORR peak potential, E p up to 325 mV vs. reversible hydrogen electrode, RHE) were more active in 0.05 M H2SO4, compared with the analogue based on PoPDA. Moreover, the activity of PmPDA- or PoPDA-based metal-polymeric composites for the ORR was higher than that for previously reported similar polyaniline-based composite, which may be due to effective formation and/or increase the number of active sites for the ORR in electrocatalysts at the expense of the presence of additional nitrogen atoms in poly(phenylenediamines).