A constraint satisfaction problem (CSP) is a general framework that can formalize various application problems in artificial intelligence. However, practical real-world problems tend to be over-constrained, and the descriptive power of the CSP is not always sufficient in formulating the problems because of various constraints involved. In this paper, we will focus on an important subclass of distributed partial CSPs called the distributed maximal CSPs that can be applied to more practical kinds of problems. Specifically, we propose a hybrid-type algorithm of solving distributed maximal CSPs using a combination of approximate and exact algorithms that yields faster optimum solutions than conventional methods. Experimental results are presented that demonstrate the effectiveness of the proposed approach. KEY WORDS distributed constraint satisfaction problem, hybrid algorithm, synchronous branch and bound, iterative distributed breakout, graph-coloring problem