  The baryon asymmetry of the universe can be explained by the
out-of-equilibrium decays of heavy right-handed neutrinos. We analyse this
mechanism in the framework of a supersymmetric extension of the Standard Model
and show that lepton number violating scatterings are indispensable for
baryogenesis, even though they may wash-out a generated asymmetry. By assuming
a similar pattern of mixings and masses for neutrinos and up-type quarks, as
suggested by SO(10) unification, we can generate the observed baryon asymmetry
without any fine tuning, if (B-L) is broken at the unification scale
\Lambda_{GUT}\sim 10^{16} GeV and, if m_{\nu_\mu} \sim 3\cdot 10^{-3} eV as
preferred by the MSW solution to the solar neutrino deficit.
