We propose a new method, called closed multidimensional sequential pattern mining, for mining multidimensional sequential patterns. The new method is an integration of closed sequential pattern mining and closed itemset pattern mining. Based on this method, we show that (1) the number of complete closed multidimensional sequential patterns is not larger than the number of complete multidimensional sequential patterns (2) the set of complete closed multidimensional sequential patterns covers the complete resulting set of multidimensional sequential patterns. In addition, mining using closed itemset pattern mining on multidimensional information would mine only multidimensional information associated with mined closed sequential patterns, and mining using closed sequential pattern mining on sequences would mine only sequences associated with mined closed itemset patterns.