Let G be a finite group and p a prime. We say that G is quasisupersoluble (resp., p-quasisupersoluble) if for every non-cyclic chief factor H/K of G (resp., for every non-cyclic chief factor H/K of G of order divisible by p), every automorphism of H/K induced by an element of G is inner. In this paper, we study the structure of quasisupersoluble and p-quasisupersoluble finite groups.