In a previous work [4], we laid the foundations of a formal compositional semantic theory for dependency grammars. In this paper, we continue this line of research with the aim of showing that the basic principles we stated in [4] allow one to deal with more advanced syntactic phenomena. We consider two cases: the relative clauses (which depend on the acl:relcl dependency relation) and the open clausal complements (which depend on the xcomp dependency relation). This leads us to revise some of the solutions advocated in [4], while at the same time generalizing some of the principles on which our theory is based