It is known that for temporal languages, such as first-order LT L, reasoning about constant (time-independent) relations is almost always undecidable. This applies to temporal description logics as well: constant binary relations together with general concept subsumptions in combinations of LT L and the basic description logic ALC cause undecidability. In this paper, we explore temporal extensions of two recently introduced families of ?weak? description logics known as DL-Lite and EL. Our results are twofold: temporalisations of even rather expressive variants of DL-Lite turn out to be decidable, while the temporalisation of EL with general concept subsumptions and constant relations is undecidable.