Implications of Improved Upper Bounds on |Delta L|=2 Processes

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.