We have studied the effect of introduction of boron, nitrogen or both elements into an electric arc on the morphology and the conductivity of the resultant carbon products. Scanning and transmission electron microscopies showed that the use of a boron-filled graphite electrode and a nitrogen gas during the arc discharge synthesis strongly affects the growth kinetics of carbon nanoparticles. The addition of boron promotes the formation of short, defective carbon nanotubes. In contrast, involvement of nitrogen in the synthesis process produces more perfect carbon nanostructures, including graphitic plates. Evaporation of a boron-filled electrode in a nitrogen atmosphere leads to BN co-doping of the carbon product. The concentration of each dopant is ca. 1 at.% and this value is twice greater than that for the cases of individual dopants. Among the studied materials, the BN-doped one possessed the highest conductivity, and this was attributed to the synergetic effect of co-doping. A substitution of carbon atoms by boron or nitrogen resulted in the p- or n-type doping of the samples, respectively. The evolution of conductivity with temperature and magnetic field showed that transport properties of the arc discharge synthesis products are strongly dependent on the charge carrier concentration, morphology and crystallinity of carbon nanoparticles.