The electronic properties of exohedrally doped double-walled carbon nanotubes (DWNTs) have been investigated using density functional theory and resonance Raman spectroscopy (RRS) measurements. First-principles calculations elucidate the effects of exohedral doping on the M@S and S@M systems, where a metallic (M) tube is either inside or outside a semiconducting (S) one. The results demonstrate that metallic nanotubes are extremely sensitive to doping even when they are inner tubes, in sharp contrast to semiconducting nanotubes, which are not affected by doping when the outer shell is a metallic nanotube (screening effects). The theoretical predictions are in agreement with RRS data on Br2- and H2SO4-doped DWNTs. These results pave the way to novel nanoscale electronics via exohedral doping.