We study multistate Schrödinger operators related to molecular dynamics. We consider potentials which do not necessarily decay and prove the absence of the singular continuous spectrum and propagation estimates which mean the scattering at speed larger than a positive constant and decay of the state with potentials higher than the considered energy at infinity. We also consider the multistate Schrödinger operators with many-body structures. We obtain the Mourre estimate and the minimal velocity estimate for the many-body operators. The lower bound of the velocity is determined by the distance between the energy and thresholds below the energy.