The topic of this thesis is the efficient implementation of the bitemporal timeslice query. It answers queries of the type: What knowledge about the state of the world at valid time, vtime, was current in the database at transaction time, ttime? Differential timeslice computation takes an existing cached timeslice as the outset and applies necessary changes to get the result of the new timeslice query. This is efficient because two timeslices with similar valid time and transaction time can be expected to have a large number of tuples in common. Differential computation has previously been applied to transaction-time databases. This scheme is extended to suit bitemporal data bases. In addition, the algorithms are generalized for history timeslices that cover a transaction or valid time period, and to n-dimensional timeslices for applications with higher dimensions of time. Some aspects of physical data storage in an implementation of the algorithm are discussed, the complexity is analyzed and compared with existing solutions. Directions for future research are given.