The model of Marsden et al. (1973) is used to investigate the effect of nongravitational forces resulting from water ice sublimation on the orbits of long-period comets. The orbits of hypothetical comets with perihelion distances of 0.005 to 4 AU are integrated numerically along initially parabolic trajectories through one perihelion passage for nongravitational forces of 10 millionths to 200 millionths the solar attraction at 1 AU and lag angles of 0, 5, and 10 deg. The results indicate that the nongravitational perturbations are possibly of equal or greater importance than planetary perturbations for comets with small perihelia and that nongravitational forces could have brought sun-grazing comets to their current orbits in two or three returns. It is concluded that nongravitational forces are likely to be found only for those long-period comets that have large nongravitational accelerations to begin with and are bright enough to be discovered early and tracked over a very long arc of their orbits.