Carbon nanotubes are metallic, semimetallic, or semiconducting, depending on their helicity. This raises the possibility of forming nanoelectronic devices by joining tubes of differing helicity. We report calculations of the electronic properties of pairs of "armchair" and "zigzag" nanotubes joined linearly. The linear junction in each case consists of a nonalternant band of 5- and 7-membered rings. For a metal-semiconductor armchair-zigzag system, charge transfer from the armchair segment to the zigzag segment is calculated to occur. The distribution of electrostatic potentials seen by any electron transferred through the system is asymmetric along the tube axis, so the system is expected to exhibit rectifying behavior. The linear junction has specific electronic properties consistent with recent measurements of rectification in carbon nanotubes.