  We show that in supersymmetric models with gauged B-L symmetry, there is a
new source for cosmological lepton asymmetry. The Higgs bosons responsible for
B-L gauge symmetry breaking decay dominantly into right-handed sneutrinos
\tilde{N} and \tilde{N}* producing an asymmetry in \tilde{N} over \tilde{N}*.
This can be fully converted into ordinary lepton asymmetry in the decays of
\tilde{N}. In simple models with gauged B-L symmetry we show that resonant/soft
leptogenesis is naturally realized. Supersymmetry guarantees quasi-degenerate
scalar states, while soft breaking of SUSY provides the needed CP violation.
Acceptable values of baryon asymmetry are obtained without causing serious
problems with gravitino abundance.
