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Using possibility measure, we study modelchecking of linear-time properties in possibilistic Kripke structures. First, the notion of possibilistic Kripke structures and the related possibility measure are introduced, then model-checking of reachability and repeated reachability linear-time properties in finite possibilistic Kripke structures are studied. Standard safety properties and ù.regular properties in possibilistic Kripke structures are introduced, the verification of regular safety properties and ù.regular properties using finite automata are thoroughly studied. It has been shown that the verification of regular safety properties and ù.regular properties in a finite possibilistic Kripke structure can be transformed into the verification of reachability properties and repeated reachability properties in the product possibilistic Kripke structure introduced in this paper. Several examples are given to illustrate the methods presented in the paper.