Now-relative temporal data play an important role in most temporal applications, and their management has been proved to impact in a crucial way the efficiency of temporal databases. Though several temporal relational approaches have been developed to deal with now-relative data, none of them has provided a whole temporal algebra to query them. In this paper we overcome such a limitation, by proposing a general algebra which is parametrically adapted to cope with the relational approaches to now-relative data in the literature, i.e., MIN, MAX, NULL and POINT approaches. Besides being general enough to provide a query language for several approaches in the literature, our algebra has been designed in such a way to satisfy several theoretical and practical desiderata: closure with respect to representation languages, correctness with respect to the "consensus" BCDM semantics, reducibility to the standard non-temporal algebra (which involves interoperability with non-temporal relational databases), implementability and ef f iciency. Indeed, the experimental evaluation we have drawn on our implementation has shown that only a slight overhead is added by our treatment of now-relative data (with respect to an approach in which such data are not present).