  Neutrinoless double beta decay ($\znbb$) induced by superparticle exchange is
investigated. Such a supersymmetric (SUSY) mechanism of $\znbb$ decay arises
within SUSY theories with R-parity non-conservation (\rp). We consider the
minimal supersymmetric standard model (MSSM) with explicit \rp terms in the
superpotential (\rp MSSM). The decay rate for the SUSY mechanism of $\znbb$
decay is calculated. Numerical values for nuclear matrix elements for the
experimentally most interesting isotopes are calculated within pn-QRPA.
Constraints on the \rp MSSM parameter space are extracted from current
experimental half-life limits. The most stringent limits are derived from data
on $^{76}$Ge. It is shown that these constraints are more stringent than those
from other low-energy processes and are competitive to or even more stringent
than constraints expected from accelerator searches.
