It is proved that for every -diffeomorphism f on a closed surface satisfying Axiom A, if f has the inverse shadowing property, then it satisfies the -transversality condition. Using this fact, we can see that the inverse shadowing property is not -generic. Also, we introduce the notion of -stable inverse shadowing and show that if f is a -stable inverse shadowing diffeomorphism on a closed surface, then (i) f is Kupka-Smale, (ii) f satisfies both Axiom A and the strong transversality condition if � , and there exists a dominated splitting on