To add time support to the relational model, both first normal form (1NF) and non-1NF approaches have been proposed. Each has associated difficulties. Remaining within 1NF when time support is added may introduce data redundancy. The non-1NF models may not be capable of directly using existing relational storage structures or query evaluation strategies. This paper describes a new, conceptual temporal data model that better captures the time-dependent semantics of the data while permitting multiple data models at the representation level. This conceptual model effectively moves the distinction between the various existing data models from a semantic basis to a physical, performance-relevant basis. We define a conceptual notion of a bitemporal relation where tuples are stamped with sets of two-dimensional chronons in transaction-time/valid-time space. We introduce a tuple-timestamped 1NF representation to exemplify how the conceptual bitemporal data model is related, by means of snapshot equivalence, with representational models. We then consider querying within the two-level framework. We first define an algebra at the conceptual level. We proceed to map this algebra to the sample representational model in such a way that new operators compute equivalent results for different representations of the same conceptual bitemporal relation. This demonstrates that the representational model is faithful to the semantics of the conceptual data model, with many choices available that may be exploited to improve performance.