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Spectrally equivalent causal (SEC) models for single-input/single-output noncausal systems are derived with the objective of estimating the noncausal impulse response. Attention is restricted to symmetric, noncausal impulse responses, and the measurements of the system output are assumed to be noisy. It is shown that by using structured SEC models, either state-space or ARMA-plus-noise, consistent estimates of the noncausal impulse response can be obtained by exploiting only the second-order statistics of the measurements. A new version of the correlation technique particularly suited to structured models is presented and analyzed. Computer simulation results are also presented to illustrate the performance of the proposed approach.