We report the results of an experimental study of the dc and ac magnetic properties of superconducting Nb thin-walled cylinders in parallel to the axis magnetic fields. The magnetization curves at various temperatures are measured. Surprisingly, at 4.5 K, for magnetic fields much lower than H c1 , avalanchelike jumps of the magnetization are observed. The position of the jumps is not reproducible and changes from one experiment to another, resembling vortex lattice instabilities usually observed for magnetic fields larger than H c1. At temperatures larger than 6.5 K, the measured magnetization curves become smooth. ac response is measured in constant and swept dc magnetic fields. A phenomenological model that describes the ac response of the surface superconducting states is proposed. This model assumes that the observed ac response in dc fields larger than H c2 is due to the relaxation of surface superconducting states with nonzero current in the walls to the state with zero current, and the existence of a critical current below which this relaxation is absent.