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.