By supporting the valid and transaction time dimensions, bitemporal databases represent reality more accurately than conventional databases. In this paper we examine the issues involved in designing efficient access methods for bitemporal databases and propose the partial-persistence and the double-tree methodologies. The partial- persistence methodology reduces bitemporal queries to partial persistence problems for which an efficient access method is then designed. The double-tree methodology "sees" each bitemporal data object as consisting of two intervals (a valid-time and a transaction- time interval), and divides objects into two categories according to whether the right endpoint of the transaction time interval is already known. A common characteristic of both methodologies is that they take into account the properties of each time dimension. Their performance is compared with a straightforward approach that "sees" the intervals associated with a bitemporal object as composing one rectangle which is stored in a single multidimensional access method. Given that some limited additional space is available, our experimental results show that the partial- persistence methodology provides the best overall performance, especially for transaction timeslice queries. For those applications that require ready, off-the-shelf, access methods the double-tree methodology is a good alternative. (Also cross-referenced as UMIACS-TR-97-24)