When two of more databases are combined into a global one, integrity may be violated even when each database is consistent with its own local integrity constraints. efficient methods for checking global integrity in data integration systems are called for: answers to queries can then be trusted, because either the global databases in known to be conssitent or suitable actions have been taken to provide for integrity checking in traditional databases to the combined case. Knowledge of local consistency is employed, perhaps together with given a priori constraints on the combination, so that only a minimal member of tuples needs to be considered. combination from scratch, integration of a new source, and absorption of local updates are dealt with for both the local-aa-view and global-as-view aproaches to data integration.