The problem of generalizing the concept of balanced realizations to infinite-dimensional continuous-time systems is considered. The realization (A,b,c) is considered on the state space \(\ell_ 2\); b and c are \(\ell_ 2\)-sequences and A generates a \(C_ 0\)-contraction semigroup. For this class of systems various \(L_{\infty}\)-approximation results are proved. Balanced realizations for infinite-dimensional systems have also been considered in previous papers [the reviewer and K. Glover, Operator theory and systems, Proc. Workshop, Amsterdam 1985, Oper. Theory, Adv. Appl. 19, 86-104 (1986; Zbl 0619.93016); and N. Young, Balanced realizations in infinite dimensions, 12th IFAC Conf., Budapest 1985 (1985)].