  We investigate Supersymmetric models where neither R parity nor lepton number
is imposed. Neutrino masses can be kept highly suppressed compared to the
electroweak scale if the $\mu$-terms in the superpotential are aligned with the
SUSY-breaking bilinear $B$-terms. This situation arises naturally in the
framework of horizontal symmetries. The same symmetries suppress the trilinear
R parity violating terms in the superpotential to an acceptable level.
