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We address the key issues of integrity constraints in temporal data within the relational framework. These issues include representation of temporal data, temporal grouping identifiers, primary keys of temporal relations and other forms of temporal integrity constraints. We extend the traditional integrity constraints to the temporal domain. In tackling subtle issues of temporality in managing time-varying data, we conceptualize that a temporal integrity constraint has a data and a temporal (time) component. The time component of a temporal integrity constraint limits the attribute values to the lifespan of an object (tuple) and it is peculiar to temporal data only. We also generalize single state integrity constraints to multistate temporal integrity constraints and apply them to existential and referential integrity.