The well-known Krylov subspace methods for model order reduction of large-scale lumped parameter systems are generalized such that they can be applied directly to a large class of linear infinite-dimensional systems including distributed parameter systems as well as delay systems. The proposed approach allows to derive finite-dimensional approximations of these infinite-dimensional systems without recourse to a large-scale lumped parameter approximation. The resulting finite-dimensional model has the usual property that prescribed moments of its transfer function coincide with the moments of the infinite-dimensional system. As in the finite-dimensional case the approach allows for a numerical efficient implementation. The results of the article are demonstrated by means of a simple example.