  The classes $\mathcal D _{\mathcal Q}$ of flat relative Mittag-Leffler
modules are sandwiched between the class $\mathcal F \mathcal M$ of all flat
(absolute) Mittag-Leffler modules, and the class $\mathcal F$ of all flat
modules. Building on the works of Angeleri H\" ugel, Herbera, and \v Saroch, we
give a characterization of flat relative Mittag-Leffler modules in terms of
their local structure, and show that Enochs' Conjecture holds for all the
classes $\mathcal D _{\mathcal Q}$. In the final section, we apply these
results to the particular setting of f-projective modules.
