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The paper advocates the interest of distinguishing between negative and positive preferences in the processing of flexible queries. Negative preferences express what is (more or less, or completely) impossible or undesirable, and by complementation state flexible constraints restricting the possible or acceptable values. Positive preferences are not compulsory, but rather express wishes; they state what attribute values would be really satisfactory. The paper discusses the handling of bipolar queries, i.e. queries involving negative and positive preferences, in the framework of possibility theory. Both ordinary queries expressed in terms of requirements, and case-based queries referring to examples, are considered in this perspective.