Abstract: If grand unification is real, searches for baryon-number violation should be included on the list of observables that may reveal information regarding the origin of neutrino masses. Making use of an effective-operator approach and assuming that nature is SU(5) invariant at very short distances, we estimate the consequences of different scenarios that lead to light Majorana neutrinos for low-energy phenomena that violate baryon number minus lepton number (B – L) by two (or more) units, including neutron-antineutron oscillations and B – L violating nucleon decays. We find that, among all possible effective theories of lepton-number violation that lead to nonzero neutrino masses, only a subset is, broadly speaking, consistent with grand unification.