A new class of bias-compensated affine-projection-like (APL) algorithms is proposed, in which a bias-compensation vector is derived to eliminate the bias caused by the noisy input. In addition, a new estimation method for the input noise variance is proposed which does not require the input–output noise variance ratio in advance. Simulations in a system identification context show that the proposed algorithms achieve significant improvements in steady-state misalignment as compared with the conventional APL algorithms.