The tcc model is a formalism for reactive concurrent constraint programming. In this paper we propose a model of temporal concurrent constraint programming which adds to tcc the capability of modeling asynchronous and non-deterministic timed behavior. We call this tcc extension the ntcc calculus. The expressiveness of ntcc is illustrated by modeling cells and asynchronous bounded broadcasting, by specifying temporal requirements such as response and invariance, and by modeling timed systems such as RCX controllers. We present a denotational semantics for modeling the strongest-postcondition behavior of ntcc processes, and, based on this semantics, we develop a proof system for proving linear temporal properties of these processes.