A model for the generation of secondary electrons and positrons within the collimated beam of energetic particles and magnetic fields flowing out of the central engines of extragalactic radio sources is proposed. It is demonstrated that if significant amounts of materials are entrained into this collimated beam as suggested recently by De Young, the proton-proton collision process may become a viable mechanism for the generation of radio-emitting electrons seen in large-scale radio jets. The model not only was successfully tested for radio jets in NGC 6251, M87, and 3C 449, but proved promising as a basis for accounting for the presence of gaps between radio cores and jets, as well as the observed absence of gradients in spectral index along some radio jets. 35 references.