  M. Tinkham and P. G. de Gennes, described in their books the existence of an
intermediate type-I superconductor as a consequence of an external surface that
affects the well known classification of superconductors into type-I and II.
Here we consider the mesoscopic superconductor where the ratio volume to area
is small and the effects of the external surface are enhanced. By means of the
standard Ginzburg-Landau theory the Tinkham-de Gennes scenario is extended to
the mesoscopic type-I superconductor. We find new features of the transition at
the passage from the genuine to the intermediate type-I. The latter has two
distinct transitions, namely, from a paramagnetic to diamagnetic response in
descending field and a quasi type-II behavior as the critical coupling is
approached in ascending field. The intermediate type-I phase proposed here, and
its corresponding transitions, reflect intrinsic features of the superconductor
and not its geometrical properties.
