  Supersymmetry offers a cold dark matter candidate, provided that lepton
number is {\em not violated by an odd number of units}. On the other hand,
lepton number violation by even (two) units gives us an attractive mechanism of
neutrino mass generation. Here we offer an explanation of this, in a
supergravity framework underlying a supersymmetric scenario, the essential
feature being particles carrying lepton numbers, which interact only
gravitationally with all other known particles. It is shown that one can have
the right amount of $\Delta L = 2$ effect giving rise to neutrino masses,
whereas the lifetime for $\Delta L = 1$ decays of the lightest supersymmetric
particle can be prolonged beyond the present age of the universe.
