  In this talk I will review the "state of the art" of the calculations of the
nuclear matrix elements (NME) of the neutrinoless double beta decays for the
nuclei 48Ca, 76Ge, 82Se, 124Sn, 128Te, 130Te and 136Xe in the framework of the
Interacting Shell Model (ISM), and compare them with the NME's obtained using
the Quasi-particle RPA approach (QRPA). I will also discuss the effect of the
competition between the pairing and quadrupole correlations in the value of
these NME's. In particular I will show that, as the difference in deformation
between parent and grand daughter grows, the NME's of both the neutrinoless and
the two neutrino modes decrease rapidly.
