Bilayer nanostructured poly(3,4-ethylenedioxythiophene) (PEDOT) and polyaniline (PANI) conducting polymer composites have been successfully prepared by oxidative polymerization of the parent monomers, aniline (An) and 3,4-ethylenedioxythiophene (EDOT), in aqueous solutions of p-toluenesulfonic acid (p-TSA). As the first step, PANI nanofibers were obtained in the p-TSA solution using ammonium persulfate (APS) as the oxidant. Subsequently, PEDOT was coated onto the PANI nanofibers by the oxidative polymerization of EDOT to form PEDOT/PANI bilayer nanofibers. The resulting nanostructured material was characterized by SEM and a range of spectroscopic methods, which confirmed that the surface layer of the synthesized materials had features typical of chemically synthesized PEDOT. The presence of the PEDOT layer increased the room temperature electrical conductivity of the PEDOT/PANI nanocomposites by 2 orders of magnitude in comparison with the parent PANI nanofibers. Moreover, PEDOT/PANI nanocomposites on a glassy carbon electrode showed stronger electrocatalytic activity for the oxidation of ascorbic acid than PANI nanofibers.