We consider the magnetic response of a normal layer (N) coating a supe
rconducting cylinder (S). The diamagnetic response of the normal layer
(proximity effect) is related to the formation of Andreev levels. At
low energies, the density of such states goes linearly to zero which e
nhances the various scattering mean-free paths. As a consequence, the
low-energy glancing states, which can skip along the outer boundary, c
an have relatively large magnetic moments that lead to a low-temperatu
re paramagnetic correction to the Meissner result. [S0031-9007(98)0649
7-7].