In supersymmetric models with lepton-number violation, hence also R-parity
violation, it is easy to have realistic neutrino masses, but then leptogene
sis becomes difficult to achieve. After explaining the general problems inv
olved, we study the details of a model which escapes these constraints and
generates a lepton asymmetry, which gets converted into the present observe
d baryon asymmetry of the Universe through the electroweak sphalerons. This
model requires the presence of certain nonholomorphic R-parity violating t
erms. For completeness we also present the most general R-parity violating
Lagrangian with soft nonholomorphic terms and study their consequences for
the charged-scalar mass matrix. New contributions to neutrino masses in thi
s scenario are discussed. (C) 2000 Elsevier Science B.V., Ail rights reserv
ed.