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A two-channel structure consisting of multiple cascades of allpass filters and directional couplers has certain desirable attributes. This paper considers adaptive algorithms for adjusting the parameters of such systems. The exemplary algorithms are motivated by an application to the compensation of polarization mode dispersion, which is a key problem in fiber optic systems. Gradient algorithms are shown to exhibit extremely slow convergence. This problem is solved by deriving a Newton-type algorithm. However, possible convergence to a local minimum emerges as a more fundamental problem. One of the conditions for local minima is specifically identified in terms of problematic parameter states.