  We show that in a large class of supersymmetric models with spontaneously
broken B-L symmetry, neutron--antineutron oscillations occur at an observable
level even though the scale of B-L breaking is very high, v_{B-L} ~ 2 x 10^{16}
GeV, as suggested by gauge coupling unification and neutrino masses. We
illustrate this phenomenon in the context of a recently proposed class of
seesaw models that solves the strong CP problem and the SUSY phase problem
using parity symmetry. We obtain an upper limit on N-\bar{N} oscillation time
in these models, \tau_{N-\bar{N}} < 10^{9} -10^{10} sec. This suggests that a
modest improvement in the current limit on \tau_{N-\bar{N}} of 0.86 x 10^8 sec
will either lead to the discovery of N-\bar{N} oscillations, or will
considerably restrict the allowed parameter space of an interesting class of
neutrino mass models.
