We compute nonadiabatic corrections for all bound and long-lived quasi-bound vibrational levels of H-2(+) and HD+ for selected rotational levels. This is done using the Bunker and Moss formalism with the correction factors computed from ab initio wave functions. The electronic wavefunctions are expanded in terms of nuclear centered Gaussian basis functions. The agreement with accurate calculations is very good: for H-2(+), the root-mean-square error in the computed dissociation energies is 0.0005 cm(-1), and, furthermore, most transition frequencies are predicted to within about 0.0001 cm(-1). For HD+, the results are not quite as good due to the uncertainties in the adiabatic correction. cm This paves the way for using these techniques to accurately predict the nonadiabatic effects for more complicated molecules. (C) 2001 American Institute of Physics.