In this paper, a notion of S*-pair wise compactness in L-bitopological space is introduced and its basical properties are studied. It is proved that the intersection of an S*-pair wise compactness L-set with a biclosed L-set ( resp., the finite sum of some S*-pair wise compactness L-sets, the continuous image of an S*-pair wise compactness L-set and the product of some S*-pair wise compactness L-sets) is S*-pair wise compactness. And for a weakly induced L-bitopological space, it is S*-pair wise compact if and only if its background space is B-pair wise compact.
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