Double-walled carbon nanotubes sorted by density gradient ultracentrifugation were examined by Raman spectroscopy and by in situ Raman spectroelectrochemistry. The sorted samples had a narrow distribution of diameters of both inner and outer tubes, which enabled a comparison of the behavior of inner metallic tubes and inner semiconducting nanotubes as a function of the applied electrochemical potential. The metallic inner tubes were efficiently doped even though they were protected from electrolyte ions by the outer wall, whereas the doping of semiconducting inner tubes was observed only at high magnitudes of the electrode potential. These results indicate that the doping response of inner tubes is predominantly controlled by inner tube electronic properties. On the other hand, the effect of electronic structure of the outer tube on the behavior of inner tube is weak. Furthermore, the efficiency of the charge transfer from outer to inner wall depends on the doping level. A low doping level corresponds to a high efficiency of the charge-transfer, while a high doping level shows low charge-transfer efficiency.