  We consider contributions of R-parity conserving softly broken supersymmetry
(SUSY) to neutrinoless double beta ($\znbb$) decay via the (B-L)-violating
sneutrino mass term. The latter is a generic ingredient of any weak-scale SUSY
model with a Majorana neutrino mass. The new R-parity conserving SUSY
contributions to $\znbb$ are realized at the level of box diagrams. We derive
the effective Lagrangian describing the SUSY-box mechanism of $\znbb$-decay and
the corresponding nuclear matrix elements. The 1-loop sneutrino contribution to
the Majorana neutrino mass is also derived.
  Given the data on the $\znbb$-decay half-life of $^{76}$Ge and the neutrino
mass we obtain constraints on the (B-L)-violating sneutrino mass. These
constraints leave room for accelerator searches for certain manifestations of
the 2nd and 3rd generation (B-L)-violating sneutrino mass term, but are most
probably too tight for first generation (B-L)-violating sneutrino masses to be
searched for directly.
