In the active database systems, whenever there are some changes on database, trigger condition should be tested. Since it causes system performance degradation, efficient evaluation of conditions in triggered rules is needed. We developed three optimization techniques: incremental evaluation, interval evaluation, and multitrigger evaluation. Incremental evaluation technique reduces the number of tuples to be investigated by looking up modified tuples only. Interval evaluation technique gives the range of the value of expression in much smaller operations. The range is used to determine whether the condition is true or not. Multi-trigger evaluation technique utilizes relationship of expressions and reduces the number of expressions to evaluate by maintaining expression graph.