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In this paper, we define the current Lie superalgebrawhere  L  is a Lie superalgebra and  A  is an associative commutative algebra with unity. we proved every skew-symmetric super-biderivation onis of the form of the centroid, if the same holds true for  L . We also proved every linear super-commuting map onbelong to Cent(), if the same holds true for  L .

Super-biderivations and linear super-commuting maps on the current Lie superalgebras