We introduce the class of possibilistic nested logic programs. These possibilistic logic programsallow us to use nested expressions in the bodies and the heads of their rules. By considering apossibilistic nested logic program as a possibilistic theory, a construction of a possibilistic logicprograming semantics based on answer sets for nested logic programs and the proof theory ofpossibilistic logic is defined. We show that this new semantics for possibilistic logic programsis computable by means of transforming possibilistic nested logic programs into possibilistic disjunctivelogic programs. The expressiveness of the possibilistic nested logic programs is illustratedby scenarios from the medical domain. In particular, we exemplify how possibilistic nested logicprograms are expressive enough for capturing medical guidelines which are pervaded of vaguenessand qualitative information.