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Existing multi-dimensional sequential pattern mining methods only discover multi-dimensional sequential pattern in databases involving one sequential dimension. Since multi-dimensional sequential patterns may exist in databases containing more than one sequential dimension, in this paper, we present algorithm PSeq-MIDim for mining multi-dimensional sequential patterns from multiple sequential dimensions with multi-dimensional information, which makes up multi-dimensional multisequence databases. PSeq-MIDim applies PSeq to mine sequential patterns from multiple sequential dimensions, then forms the corresponding projected multi-dimensional database for each sequential pattern, and uses MIDim to mine multi-dimensional patterns within projected databases. PSeq performs sequential pattern mining from one sequential dimension, and then propagates the mined sequential patterns to other sequential dimension. Furthermore, the mined sequential patterns are represented as a lattice structure to provide guidelines for mining sequential patterns across multiple sequential dimensions. MIDim, which scans projected database only one time, makes the best of prefix-index technique for focused searching and finds multi-dimensional patterns rapidly. The experimental results show that PSeq-MIDim is efficient to find multi-dimensional sequential patterns from multi-dimensional multi-sequence databases.