  We introduce the notion of an enriched fibration, i.e. a fibration whose
total category and base category are enriched in those of a monoidal fibration
in an appropriate way. Furthermore, we provide a way to obtain such a
structure, starting from actions of monoidal categories with parameterized
adjoints. The motivating goal is to capture certain example cases, like the
fibration of modules over algebras enriched in the opfibration of comodules
over coalgebras.
