The dynamical evolution of short-period objects having perihelia at small heliocentric distances is discussed. We have investigated the motion of multiple-apparition members of the Marsden and Kracht sungrazing groups. The orbital evolution of these objects on timescales < 10 Kyr is mainly determined by the Kozai-Lidov secular perturbations. These objects are dynamically connected with high-inclination near-Earth objects. On the other hand, we have found several observed near-Earth objects that evolve in the same way, reaching small perihelion distances on short timescales in the past.