Mining association rules is an important data mining problem. There have been many algorithms proposed for efficient discovery of association rules in large databases. However, very little work has been done on maintenance of discovered association rules. When users interactively mine association rules, they may have to continually tune two thresholds, minimum support and minimum confidence, which describe the users' special interestingness. In this paper, two incremental updating algorithms——IUA and PIUA are presented for such efficient maintenance problem of association rules.