  Motivated by results from short-baseline neutrino oscillation data, we study
neutrino masses and mixing in U(1)' supersymmetric models with R-parity
breaking. Whether R-parity is broken spontaneous or through (effective)
bilinear terms in the Lagrangian, the breaking terms induce mixing between the
neutralinos and neutrinos, creating a scenario in which some neutralinos can be
heavy, and some light. Both the right-handed neutrino and the singlino
(fermionic partner of the additional singlet Higgs field) can be light, and act
as sterile neutrinos, which reconcile some of the anomalies observed in solar
baseline and reactor experiments. We show that, scanning a large range of the
parameter space satisfying solar and atmospheric neutrino constraints, the mass
and mixing parameters of the sterile neutrinos are very restrictive, leading to
some predictive features for the U(1)' scenarios.
