The purpose of this work is to study a generalisation of Dung’s abstract argumentation frameworks that allows representing positive interactions (called supports). The notion of support studied here is based in the intuition that every argument must be supported by some chain of supports from some special arguments called prima-facie. The theory developed also allows the representation of both recursive attacks and supports, that is, a class of attacks or supports whose targets are other attacks or supports. We do this by developing a theory of argumentation where the classic role of attacks in defeating arguments is replaced by a subset of them, which is extension dependent and which, intuitively, represents a set of “valid attacks” with respect to the extension. Similarly, only the subset of “valid supports” is allowed to support other elements (arguments, attacks or supports). This theory displays a conservative generalisation of Dung’s semantics (complete, preferred and stable) and also of their principles (conflict-freeness, acceptability and admissibility). When restricted to finite non-recursive frameworks, we are also able to prove a one-to-one correspondence with Evidence-Based Argumentation (EBA). When supports are ignored a one-to-one correspondence with Argumentation Frameworks with Recursive Attacks (AFRA) semantics is also established.