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, ��_{N-\bar{N}} < 10^{9} -10^{10} sec. This suggests that a modest improvement in the current limit on ��_{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.

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