An incremental technique and a fast algorithm FUP have been proposed previously for the update of discovered single-level association rules (SLAR). In this study, a more efficient algorithm FUP*, which generates a smaller number of candidate sets when comparing with FUP, has been proposed. In addition, we have demonstrated that the incremental technique in FUP and FUP* can be generalized to some other kdd systems. An efficient algorithm MLUp has been proposed for this purpose for the updating of discovered multi-level association rules (MLAR). Our performance study shows that MLUp has a superior performance over ML-T2 in updating discovered MLAR.