The nuclear matrix elements for the Ge~' Se, ' Se~Kr, ' Se~' Kr, and ' Kr~' Sr double p decay were calculated in a shell-model space consisting of the Og9/2 1P,&2, lp3&2, and Ofsqz orbitals for both protons and neutrons, and using an effective interaction that contained secondorder corrections. For light intermediate neutrinos our results are in agreement with the previously available Los Alamos matrix elements. We have, however, obtained nuclear matrix elements relevant for intermediate heavy neutrinos, Higgs bosons, and supersymmetric particles. Using these matrix elements and the available experimental limits for neutrinoless double p decay, we obtained the following mass limits:~(m, )~&1.1 eV, ((1/MN)) '&1.0X10' GeV, m &740 GeV, and m, & 360 GeV for the light left-handed and heavy right-handed neutrinos, the squark, and the selectron, respectively. We also obtained the limits~g~&4)&10 ' and r)&1.3x10 for the majoron neutrino coupling and the admixture of right-handed currents, respectively.