  The coherent phenomena in mesoscopic cylindrical normal metal (N) -
superconductor (S) structures have been investigated theoretically. The
magnetic moment (persistent current) of such a structure has been calculated
numerically and (approximately) analytically. It is shown that the current in
the N layer corresponding to the free-energy minimum is always diamagnetic. As
the field increases, the magnetic moment (current) exhibits jumps at certain
values of the trapped magnetic flux and the NS structure changes to a state
with smaller absolute value of the diamagnetic moment. This occurs when the
persistent current is unable to screen the external field. The magnetic moment
increase stepwise and the system changes into a new stable state. The magnetic
field penetrates into a larger volume of the N layer. The state has smaller
absolute value of the diamagnetic moment. Experimentally, this is interpreted
as the presence of a paramagnetic addition in the system (paramagnetic
reentrant effect). The results obtained are in qualitative agreement with the
experiments conducted by P. Visani et al. [Phys. Rev. Lett. 65, 1514 (1990)].
