  We propose a new class of leptogenesis bounds on the spontaneous symmetry
breaking of global lepton number. These models have a generic feature of
inducing new lepton number violating interactions, due to the presence of the
Majorons. We analyzed the singlet Majoron model with right-handed neutrinos and
find that the lepton number should be broken above 10^5 GeV to realize a
successful leptogenesis because the annihilations of the right-handed neutrinos
into the massless Majorons and into the standard model Higgs should go out of
equilibrium before the sphaleron process is over. We then argue that this type
of leptogenesis constraint should exist in the singlet-triplet Majoron models
as well as in a class of R-parity violating supersymmetric Majoron models.
