  We consider various possibilities for generating neutrino masses in
supersymmetric models with an additional U(1)' gauge symmetry. One class of
models involves two extra U(1)' x U(1)'' gauge symmetries, with U(1)'' breaking
at an intermediate scale and yielding small Dirac masses through
high-dimensional operators. The right-handed neutrinos N^c_i can naturally
decouple from the low energy U(1)', avoiding cosmological constraints. A
variant version can generate large Majorana masses for N^c_i and an ordinary
see-saw. We secondly consider models with a pair of heavy triplets which couple
to left-handed neutrinos. After integrating out the heavy triplets, a small
neutrino Majorana mass matrix can be generated by the induced
non-renormalizable terms. We also study models involving the double-see-saw
mechanism, in which heavy Majorana masses for N^c_i are associated with the
TeV-scale of U(1)' breaking. We give the conditions to avoid runaway directions
in such models and discuss simple patterns for neutrino masses.
