In minimal SUSY GUT models the R-parity breaking terms are severely co
nstrained by SU(5) gauge invariance. We consider the particular case w
here the explicit R-parity breaking occurs only via dimension-2 terms
of the superpotential. This model possesses only three R-parity breaki
ng parameters. We have studied the predictions of this model for the n
eutrino masses and mixing angles at the one-loop level within the fram
ework of a radiatively broken unified supergravity model. We find that
this model naturally yields masses and mixing angles that can explain
the solar and atmospheric neutrino problems. In addition, there are r
egions in parameter space where the solution to the solar neutrino puz
zle is compatible with either the LSND result or the existence of sign
ificant hot dark matter neutrinos.