  The neutrinoless double beta ($\znbb$) decay is analyzed within the Minimal
Supersymmetric Standard Model with explicit R-parity violation (\rp MSSM). We
have found new supersymmetric contributions to this process and give the
complete set of relevant Feynman diagrams. Operators describing $0^+
\longrightarrow 0^+$ nuclear transitions induced by the supersymmetric
interactions of the \rp MSSM are derived. These operators can be used for
calculating the $\znbb$ decay rate applying any specific nuclear model wave
functions.
