Defeat between arguments is a combination of two basic elements: a conflict relation and a preference order. We present a framework for argumentation where two kinds of defeat relation are present, depending on the outcome of a preference function. An argument A is a proper defeater of B, if both arguments are in conflict, and A is preferred to B according to. A is a blocking defeater of B, if they are in conflict and both arguments are incomparable or indistinguishable. We define a function to caracterize the set of accepted argument in the framework. This function also provide a method for identifying controversial situations.