The authors study infinite-dimensional linear systems with unbounded control and observation operators. The concepts of admissible control and observation operators, and well-posed linear systems is generalized in order to treat control and observation operators which are not admissible in the usual sense. This leads to the notions of \(\beta\)-admissibility and \((\beta,\gamma)\)-well-posed linear systems. In order to characterize internal stability a modified transfer function is introduced. The main result of this paper concerns an equivalence between internal and external stability. For the special case of a well-posed linear system \((A,B,C)\) satisfying the determined growth condition the main result can be stated as follows: the system is internally stable if and only if the system is stabilizable, detectable and the modified transfer function \(\lambda\mapsto C(\mu-A)^{-1}(\lambda-A)^{-1}B\) is analytic and bounded on the open right half plane.