Abstract. This article describes an attempt to implement a constraintbased dependency grammar for Czech, a language with rich morphology and free word order, in the formalism Extensible Dependency Grammar (XDG). The grammar rules are automatically inferred from the Prague Dependency Treebank (PDT) and constrain dependency relations, modification frames and word order, including non-projectivity. Although these simple constraints are adequate from the linguistic point of view, their combination is still too weak and allows an exponential number of solutions for a sentence of n words.