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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 exponentiabilityand microlinearity for Frolicher spaces. In this paper we will relativize it soas to obtain the theory of fiber bundles for Fr\"olicher spaces. It is shownthat any Weil functor naturally gives rise to a fiber bundle. We will see thatthe category of fiber bundles over a fixed Fr\"olicher space M and their smoothmappings over M is cartesian closed. We will see also that the category ofvector bundles over M and their smooth linear mappings over M is cartesianclosed. It is also shown that the tangent bundle functor naturally yields avector bundle.

Relative Microlinearity -Towards the general theory of fiber bundles for Frolicher spaces