  We discuss implications of improved upper bounds on the $|\Delta L|=2$
processes (i) $K^+ \to \pi^- \mu^+ \mu^+$, from an experiment at BNL, and (ii)
$\mu^- \to e^+$ conversion, from an experiment at PSI. In particular, we
address the issue of constraints on neutrino masses and mixing, and on
supersymmetric models with R-parity violation.
