Abstract. We investigate the computational complexity of reasoning over temporal extensions of conceptual data models. The temporal conceptual models we analyse include the standard UML/EER ISA between entities and relationships, disjointness and covering, cardinality constraints and their refinements, multiplicity and key constraints; in the temporal dimension, we have timestamping, evolution and transition constraints, as well as lifespan cardinalities. We give a nearly comprehensive picture of the impact of these constraints on the complexity of reasoning, which can range from NLOGSPACE to undecidability.