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We study the (p,q)5-brane dynamics from the viewpoint of Matrix string theoryin the T-dualized ALE background. The most remarkable feature in the(p,q)5-brane is the existence of ``fractional string'', which appears as theinstanton of 5-brane gauge theory. We approach to the physical aspects offractional string by means of the two types of Matrix string probes: One ofwhich is that given in hep-th/9710065. As the second probe we present theMatrix string theory describing the fractional string itself. We calculate themoduli space metrics in the respective cases and argue on the specificbehaviors of fractional string. Especially, we show that the ``joining''process of fractional strings can be realized as the transition from theCoulomb branch to the Higgs branch of the fractional string probe. In thisargument, we emphasize the importance of some monodromies related with thetheta-angle of the 5-brane gauge theory.Comment: 21 pages, Late

Fractional strings in (p,q) 5-brane and quiver matrix string theory