In this paper, the characterization of right and left quasi-Frobenius categories, has been given. Let C be a small preadditive category, C* the dual category of C. It has shown, that the following conditions are equivalent: (i) C is right and left quasi-Frobenius; (ii) All flat C-modules and all flat C*-modules are injective; (iii) All injective C-modules and all injective C*-modules are projective.