We apply the ab initio no-core nuclear shell model to solve the six-nucleon
systems, Li-6 and He-6, interacting by realistic nucleon-nucleon (NN) pote
ntials. In particular, we present the first results for A = 6 with the nonl
ocal CD-Bonn NN potential. The resulting Li-6 binding energy -29.3(6) MeV a
nd the excitation spectra improve the agreement between the theory and expe
riment compared to results with local NN potentials, but the need for the i
nclusion of a real three-body interaction and/or further improvement of the
NN forces remains. We predict properties of the He-6 dipole modes, a subje
ct of current controversy.