Vector leptons (N,E) are present in both E/sub 6/ and SO(18) unified theories. We derive linear relations between the masses of these vector leptons and ordinary leptons, and their mixing angles. We calculate the amplitudes for such processes as E/sup +/E/sup -/..-->..E/sup +/E/sup -/ and e/sup +/E/sup -/..-->..boson-boson. We find that these relations are crucial in unitarity considerations for the latter reactions. We also find that, unlike the case of fourth-generation leptons, no bounds from perturbative unitarity can be put on the masses of the vector leptons.