  Four different supersymmetric models based on SU(2)_L X U(1)_R X U(1)_B-L and
SU(2)_L X SU(2)_R X U(1)_B-L gauge symmetry groups are studied. U(1)_B-L
symmetry is broken spontaneously by a vacuum expectation value (VEV) of a
sneutrino field. The right-handed gauge bosons may obtain their mass solely by
sneutrino VEV. The physical charged lepton and neutrino are mixtures of
gauginos, higgsinos and lepton interaction eigenstates. Explicit formulae for
masses and mixings in the physical lepton fields are found. The spontaneous
symmetry breaking mechanism fixes the trilinear R-parity breaking couplings.
Only some special R-parity breaking trilinear couplings are allowed. There is a
potentially large trilinear lepton number breaking coupling - which is unique
to left-right models - that is proportional to the SU(2)_R gauge coupling g_R.
The couplings are parametrized by few mixing angles, making the spontaneous
R-parity breaking a natural ``unification framework'' for R-parity breaking
couplings in SUSYLR models.
