In this paper, we extend the basic abstract argumentation framework proposed by Dung, by taking into account two independent kinds of interaction between arguments: a defeat relation and a support relation. In that new framework, called a bipolar argumentation framework, we focus on the concept of acceptability and propose new semantics defined from characteristic properties that a set of arguments must satisfy in order to be an output of the argumentation process. We generalize the well-known stable and preferred semantics by enforcing the coherence requirement for an acceptable set of arguments.