This correspondence attempts to derive the exact implementation of two nonlinear active noise control (ANC) algorithms, viz. FSLMS and VFXLMS. The concept of reutilizing a part of the computations performed for the first sample while computing the next sample, for a block length of two samples, is exploited here to implement the fast and exact versions of the FSLMS and VFXLMS algorithms which are computationally efficient. Detailed computational complexity analysis for both addition and multiplication requirements is presented to show the advantage of the proposed algorithms. Appropriate simulation experiments are carried out to compare the performance equivalence of the proposed fast algorithms with their original versions. © 2008 IEEE.