Because the effective ''area'' of the Neptunian rings is larger than that of the inner moons, the sweeping of energetic particles by the rings is perhaps the dominant process for particle loss in the magnetosphere within 5 RN. In this paper we describe a theory for calculating the absorption probability of energetic charged particles by the rings. We include the effects of a large tilt and an offset between the planet and dipole centers. We find that the probability of absorption for protons is so high that the sweeping lifetime is only a few times the gradient-curvature drift period. For electrons the sweeping lifetime is even less. The pitch angle dependence for sweeping manifests itself strongly only at large equatorial pitch angles. Lower-energy particles have higher absorption rates by the rings. ¿American Geophysical Union 1991