  In our previous papers [Far East Journal of Mathematical Sciences, 35 (2009),
211-223] and [International Journal of Pure and Applied Mathematics, 60 (2010),
15-24] we have developed the theory of Weil prolongation, Weil exponentiability
and microlinearity for Frolicher spaces. In this paper we will relativize it so
as to obtain the theory of fiber bundles for Fr\"olicher spaces. It is shown
that any Weil functor naturally gives rise to a fiber bundle. We will see that
the category of fiber bundles over a fixed Fr\"olicher space M and their smooth
mappings over M is cartesian closed. We will see also that the category of
vector bundles over M and their smooth linear mappings over M is cartesian
closed. It is also shown that the tangent bundle functor naturally yields a
vector bundle.
