This paper presents a new block gradient-based adaptive algorithm for Infinite Impulse Response (IIR) adaptive filters. In contrast with the Recursive Prediction Error (RPE) algorithm, the proposed algorithm employs more accurate gradient estimates. The gradients are calculated based on sampled data blocks, within which the filter coefficients are kept constant. The proposed approach is characterised by improved steady-state performance and reduced computational complexity when compared with the conventional RPE algorithm. © 1995.