In a temporal database, object properties and associations evolve very irregularly in time. Different evaluations of data objects with different valid intervals need to be recorded and processed for different temporal instances and their associations. Their intervals need to be aligned in order to find the common intervals in which the combined data are valid. Efficiency can be gained if, in every step of the traversals and manipulations, a minimal number of temporal instances is produced. This paper presents a set of semantics-based time-alignment operations defined as time-computation construct. They can be used as guides to determine the proper alignment operations that should be used to achieve efficient query processing. Five primitive time-alignment operations are defined in this paper. They can be combined and used to efficiently support different temporal query situations. As a byproduct of implementing a parallel temporal query processor on an nCUBE2 computer, we found that these time-alignment primitives and their combinations can be implemented efficiently using a memory mapping technique. We present this implementation technique and analyze its order of complexity. (C) Elsevier Science Inc. 1997.