Default rules express concise pieces of knowledge having implicit exceptions, which is appropriate for reasoning under incomplete information. Specific rules that explicitly refer to exceptions of more general rules can then be handled in this non-monotonic setting. However, there is no assessment of the certainty with which the conclusion of a default rule holds when it applies. We propose a formalism in which uncertain default rules can be expressed, but still preserving the distinction between the defeasibility and uncertainty semantics in a two steps processing. Possibility theory is used for representing both uncertainty and defeasibility. The approach is illustrated in persistence modeling and in fuzzy default reasoning problems.