We apply first-principles calculations to investigate the interplay between electronic and magnetic properties of carbon nanotubes with line defects. We consider three types of defects: lines of C--O--C epoxy groups, and defects resulting from the substitution of the oxygen atoms by CH2 or C2H4 divalent radicals. We find that the line defects behave as pairs of coupled graphene edge states, and a variety of electronic and magnetic ground states is predicted as a function of defect type, nanotube diameter, and a possibly applied transverse electric field.