[en] A combination of geometric and algebraic methods is used to prove asymptotic completeness for Schroedinger-type equations with potential not vanishing at infinity along hyperboloids (in spacetime), and with the free Hamiltonian given by the (not bounded below) relativistic (mass)² operator. The proof is based on the use of a modified form of local compactness and additional geometric properties of asymptotic scattering states which are needed to distinguish them from states 'trapped' inside some hyperboloid for all times. (orig.)