Fast algorithms for computing the forward and inverse sequency-ordered complex Hadamard transforms (SCHT) in a sliding window are presented. The first algorithm consists of decomposing a length- N inverse SCHT (ISCHT) into two length-N/2 ISCHTs. The second algorithm, calculating the values of window i + N/4 from those of window i and one length-N/4 ISCHT and one length-N/4 Modified ISCHT (MISCHT), is implemented by two schemes to achieve a good compromise between the computation complexity and the implementation complexity. The forward SCHT algorithm can be obtained by transposing the signal flow graph of the ISCHT. The proposed algorithms require O(N) arithmetic operations and thus are more efficient than the block-based algorithms as well as those based on the sliding FFT or the sliding DFT. The application of the sliding ISCHT in transform domain adaptive filtering (TDAF) is also discussed with supporting simulation results.