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This paper deals with the problem of solving efficiently structured CSPs. It is well known that (hyper)tree-decompositions offer the best approaches from a theoretical viewpoint, but from the practical viewpoint, these methods do not offer efficient algorithms. Therefore, we introduce here a framework founded on coverings of CSP by acyclic hypergraphs. We study their properties and relations, and evaluate theoretically their interest with respect to the solving of structured problems. This framework does not define a new decomposition, but makes easier a dynamic management of the CSP structure during the search, and so an exploitation of dynamic variables ordering heuristics in the solving method. Thus, we provide a new complexity result which outperforms significantly the previous one given in the literature about heuristics for solving a decomposed problem. Finally, we present experimental results to assess the practical interest of these notions.