We consider a multiobjective mathematical programming problem with inequality and equality constraints, where all functions are locally Lipschitz. An approximate strong Karush-Kuhn-Tucker (ASKKT for short) condition is defined and we show that every local efficient solution is an ASKKT point without any additional condition. Then a nonsmooth version of cone-continuity regularity is defined for this kind of problem. It is revealed that every ASKKT point under the cone-continuity regularity is a strong Karush-Kuhn-Tucker (SKKT for short) point. Correspondingly, the ASKKTs and the cone-continuity property are defined and the relations between them are investigated.
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