We have investigated the many-body effects in a molecular theory to determine simultaneously nuclear and electronic wave functions without the Born-Oppenheimer (BO) approximation. We first apply the many-body perturbation theory using the electron-nucleus and nucleus-nucleus interactions to the non-BO theory and show the importance of the electron-nucleus correlation rather than the nucleus-nucleus one. We next combine the non-BO theory with the coupled cluster double and Brueckner double methods using the one-electron plus one-nucleus excitation operators. (C) 2003 American Institute of Physics.