A new adaptive algorithm for system identification and adaptive signal processing has been proposed in this paper. The algorithm can be viewed as a combination of the output-error type and the equation-error type of identifier (that is, a combination of the IIR adaptive filter and the FIR adaptive filter in signal-processing applications). It has been shown both mathematically and by computer simulation that the proposed algorithm can guarantee the globally asymptotical stability. The transient behaviour of the algorithm is better than the conventional output-error type of identifier, especially in the case where the system (signal model) has its eigenvalues on the unit circle. Under certain conditions on the system model (signal model), no moving average (MA) smoothing of the generalized error is needed for the strictly positive realness (SPR) conditions.