This paper concerns the convergence of a class of rational approximations for delay systems of the form exp (— sT) M(s), where M(s) is a strictly proper rational transfer matrix. The rationale for reducing the order of G(s) is to replace exp (— sT) in G(s) by the class of all-pass/low-pass Pade approximations. The L2and Lmconvergence in the frequency domain are established under mild conditions on M(s) (and hence impulse response in the L2case). For scalar M(s), the convergence is achieved at an optimal rate. Error bounds for the approximants are obtained which provide a priori estimates for the errors.