Balanced-realizations are attractive for adaptive filtering, due to their minimum parameter sensitivity and due to their usefulness in model-reduction problems. A balanced-realization based adaptive IIR filtering algorithm is presented. The proposed algorithm uses a stochastic-gradient based search technique to minimize the output error. The algorithm inherently guarantees that the adaptive filter will always remain stable, which obviates the need for the usual stability check after adaptation. Since the algorithm minimizes the output error, the resulting estimates are unbiased. We try to avoid possible convergence to local minima of the output-error surface by using "good" initial estimates, as obtained from equation-error based adaptive filters. Simulation results show that the proposed algorithm converges to the global minimum of the output-error surface.