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Item On Closed Space Curves in Minkowski Space-Time E v n(Springer (India) Private Ltd., 2012) Arı Z.; Önder M.A criterion for a 3-space curve to be closed has been presented in "Chung: Proc. Am. Math. Soc. 83, 357-361 (1981)". In this paper, following same procedure, we give generalization of the criterion for a 3-space curve to an n-space curve to be closed in Minkowski space-time E v n . Furthermore, we apply this criterion for a curve lying on an oriented surface in the Minkowski 3-space E 1 3 as an application. © 2012 Foundation for Scientific Research and Technological Innovation.