  The constraints on an R-parity violating supersymmetric theory arising from
the recent SuperKamiokande results on atmospheric neutrinos are studied, with
special reference to a scenario with bilinear R-parity violating terms.
Considering both the fermionic and scalar sectors, we find that a large area of
the parameter space is allowed, in terms of both the lepton-number violating
entries in the superpotential and the soft R-violating terms in the scalar
potential, and that no fine-tuning is required. However, the need to avoid
flavour changing neutral currents puts additional restrictions on the theory,
requiring either the R-violating terms in the superpotential to be smaller than
the R-conserving ones, or a hierarchy in the R-violating parameters for
different lepton flavours in the superpotential.
