  We show that in minimal supersymmetric standard model (MSSM) with R-parity
breaking as well as in the left-right symmetric model, there are new observable
contributions to neutrinoless double beta decay arising from hitherto
overlooked diagrams involving the exchange of one W boson and one scalar boson.
In particular, in the case of MSSM, the present experimental bounds on
neutrinoless double beta decay lifetime improves the limits on certain R-parity
violating couplings by about two orders of magnitude. It is shown that similar
diagrams also lead to enhanced rates for $\mu^-\rightarrow e^+$ conversion in
nuclei, which are in the range accessible to ongoing experiments.
