Among the variety of proposals currently making the dependency perspective on grammar more concrete, there are several treebanks whose annotation exploits some form of Relational Structure that we can consider a generalization of the fundamental idea of dependency at various degrees and with reference to different types of linguistic knowledge. The paper describes the Relational Structure as the common underlying representation of treebanks which is motivated by both theoretical and task-dependent considerations. Then it presents a system for the annotation of the Relational Structure in treebanks, called Augmented Relational Structure, which allows for a systematic annotation of various components of linguistic knowledge crucial in several tasks. Finally, it shows a dependency-based annotation for an Italian treebank, i.e. the Turin University Treebank, that implements the Augmented Relational Structure. 1