Flux penetration measurements on bulk specimens of DyBa2Cu3O7 were performed at 4.2 and 77 K in magnetic fields up to 7 Tesla using Campbell's ac method. There are two distinct regions of flux penetration: 1. For very low ac fields (< 1 mT) a certain amount of flux penetrates the specimen and is then moved almost reversibly as the ac field is increased. 2. For higher ac fields at 4.2 K flux penetration occurs in a manner consistent with the critical state model with negligible surface contribution. At 77 K the surface contribution is very large, resulting in an apparent penetration of 50% or more with comparatively small bulk current densities.