Many problems in multi-agent systems can be described as distributed CSPs. However, some real-life problem can be over-constrained and without a set of consistent variable values when described as a distributed CSP. We have presented the distributed partial CSP for handling such an over-constrained situation and the distributed maximal CSP as a subclass of distributed partial CSP. In this paper, we first show another subclass of distributed partial CSP, the distributed hierarchical CSP. Next, we present a series of new algorithms for solving a distributed hierarchical CSP, each of which is designed based on our previous distributed constraint satisfaction algorithms. Finally, we evaluate the performance of our new algorithms on distributed 3-coloring problems in terms of optimality and anytime characteristics. The results show that our new algorithms perform much better than the previous algorithm for finding an optimal solution and produce good results for anytime characteristics.