Neutrinoless double beta (beta beta(0v)) decay is considered within bilinear Rparity breaking supersymmetry, including the full oneloop corrections to the neutrinoneutralino mass matrix. Expected rates for beta beta(0v) decay in this model are discussed in light of recent atmospheric and solar neutrino data. We conclude that (a) treelevel calculations for beta beta(0v) decay within the bilinear model are not reliable in the range of parameters preferred by current solar and atmospheric neutrino problems. And (b) if the solar and atmospheric neutrino problems are to be solved within bilinear Rparity violating SUSY the expected rates for beta beta(0v) decay are very low; the effective Majorana neutrino mass at most 0.01 eV and typical values being one order of magnitude lower. Observing beta beta(0v) decay in the next round of experiments therefore would rule out the bilinear Rparity violating supersymmetric model as an explanation for solar and atmospheric neutrino oscillations, as well as any hierarchical scheme for neutrino masses, unless new neutrino interactions are present.
