Low correlation zone (LCZ) and zero correlation zone (ZCZ) aperiodic complementary sequence (ACS) sets have potential applications in multi-carriers CDMA communication systems as they can support more users than conventional complementary sequence sets. In this paper, a generic construction of LCZ-ACS and ZCZ-ACS sets are presented. The length of LCZ/ZCZ is flexible and thus the presented LCZ-ACS and ZCZ-ACS sets are more useful in applications.