Abstract-We present order K afne projection and recursive least squares adaptive lters employing partial update schemes. The starting point of the work is the MMax tap-selection criterion in which, given a lter length L, only M coefcients are updated that correspond to the M largest magnitude elements of the regression vector. We extend this approach from its existing form of MMax-NLMS to new afne projection and recursive least squares schemes with supporting analysis and simulation results. We discuss the computational complexity of these approaches for two alternative sort procedures. Finally, we extend the MMax criterion to a multichannel case by introducing an exclusivity constraint and show the effectiveness of the resulting XM tapselection criterion for application to stereophonic acoustic echo cancellation.