We consider the use of adaptive Volterra filters, implemented in the form of multichannel filter banks, as nonlinear active noise controllers. In particular, we discuss the derivation of filtered-X affine projection algorithms for homogeneous quadratic filters. According to the multichannel approach, it is then easy to pass from these algorithms to those of a generic Volterra filter. It is shown in the paper that the AP technique offers better convergence and tracking capabilities than the classical LMS and NLMS algorithms usually applied in nonlinear active noise controllers, with a limited complexity increase. This paper extends in two ways the content of a previous contribution published in Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP '03), Grado, Italy, June 2003. First of all, a general adaptation algorithm valid for any order of affine projections is presented. Secondly, a more complete set of experiments is reported. In particular, the effects of using multichannel filter banks with a reduced number of channels are investigated and relevant results are shown.