We develop a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei, by combining the resonating-group method with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach preserves translational symmetry and Pauli principle. We present phase shifts for neutron scattering on 3H, 4He, and 10Be and proton scattering on 3,4He, using realistic nucleon-nucleon potentials. Our A=4 scattering results are compared to earlier ab initio calculations. We demonstrate that a proper treatment of the coupling to the n-10Be continuum is successful in explaining the parity-inverted ground state in 11Be.