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The monic normalization equation-error (MNEE) algorithm for adaptive IIR filtering is applied to the reduced-order identification. It is shown that the parameter estimates converge to the solution of the well-known eigenvalue equation. Unlike the ordinary equation-error adaptive IIR filter, the MNEE adaptive IIR filter matches the second-order response as well as the impulse response of an unknown system. The simulation results confirm that the simple MNEE algorithm can provide a stable, unbiased estimate in the reduced-order case.