Superior performance of fast recursive least squares (RLS) algorithms over the descent-type least mean square (LMS) algorithms in the adaptation of FIR systems has not been realized in the adaptation of IIR systems. This is the result of having noisy observations of the original system output resulting in significantly biased estimates of the system parameters when this noisy signal is used in the adaptive system. Here, we propose an adaptive IIR system structure consisting of two parts: a two-channel FIR adaptive filter whose parameters are updated by the rotation-based multichannel least squares lattice (QR-MLSL) algorithm, and an adaptive régresser that provides more reliable estimates to the original system output based on previous values of the adaptive system output and noisy observation of the original system output. Two different regressors are investigated, and robust ways of adaptation of the régresser parameters are proposed. The performances of the proposed algorithms are compared with composite régresser (CR) and bias remedy least mean square equation error (BRLE) algorithms that are LMS-type successful adaptation algorithms, and it is found that in addition to the expected convergence speedup, the proposed algorithms provide better estimates to the system parameters at low SNR value. In addition, the extended Kaiman filtering approach is tailored to our application. Comparison of the proposed regressor-based algorithms with the extended Kaiman filter approach revealed that the proposed approaches provide improved estimates in systems with abrupt parameter changes. ©1993 IEEE.