Summary: In this letter we present steady-state analyses of a gradient algorithm (GA) for second-order adaptive infinite impulse response (IIR) notch filters. A method for deriving more accurate estimation mean square error (MSE) expressions than the recently proposed method is presented. The method is based on the estimation error power spectral density (PSD). Moreover, an expression for the estimation bias for the adaptive IIR notch filter with constrained poles and zeros is shown to be obtained from the estimation MSE expression. Simulations are presented to confirm the validity of the analyses.