Constraint satisfaction problems (CSPs) provide a model often used in Artificial Intelligence. Since the problem of the existence of a solution in a CSP is an NP-complete task, many filtering techniques have been developed for CSPs. The most used filtering techniques are those achieving arc-consistency. Nevertheless, many reasoning problems in AI need to be expressed in a dynamic environment and almost all the techniques already developed to solve CSPs deal only with static CSPs. So, in this paper, we first define what we call a dynamic CSP, and then, give an algorithm achieving arc-consistency in a dynamic CSP. The performances of the algorithm proposed here and of the best algorithm achieving arc-consistency in static CSPs are compared on randomly generated dynamic CSPs. The results show there is an advantage to use our specific algorithm for dynamic CSPs in almost all the cases tested.