An algorithm is presented for identifying state-space models from frequency-domain data. The main advantage of this approach is that it avoids windowing distortions associated with other frequency-domain methods. Other advantages are that an arbitrary frequency weighting can be introduced to shape the estimation error, and the system order can be overspecified. The numerical properties are demonstrated on real physical data taken on a complex flexible structure, leading to the successful identification of a multivariable (four-input/three-output) 100-state model over a bandwidth of 100 Hertz. The results indicate that the algorithm would be useful in applications requiring the accurate identification of high-order systems over wide bandwidths.