In this paper, the notions of f -injective and f ∗-injective modules are indroduced.
Elementary properties of these modules are given. For instance, a ring R is coherent
iff any ultraproduct of f -injective modules is absolutaly pure.We prove that the class


∗ of f ∗-injective modules is closed under ultraproducts. On the other hand,

∗ is not
axiomatisable. For coherent rings R,

∗ is axiomatisable iff every χ0 -injective module
is f ∗-injective. Further, it is shown that the class
of f -injective modules is axiomatisable
iff R is coherent and every χ0-injectivemodule is f -injective. Finally, an f -injective
module H, such that every module embeds in an ultraprower of H, is given.