The claim made in this paper is that in a formal description of language, it is possible and useful to work with dependency-based underlying representations of sentences (tectogrammatical representations) meeting the condition of projectivity. The reasons for the inclusion of this condition into the definition of the tectogrammatical representations are both formally and empirically sound (Section 1). An analysis of the material offered by the Prague Dependency Treebank with annotations of the underlying syntactic structure of sentences (described in Section 2) has led to an interesting classification of non-projective constructions in Czech (Section 3). It documents that most (types of) constructions that appear to be non-projective in the surface shape of sentences can be described by means of projective trees. The realization of the surface word order (with the use of movement rules) is then relegated to the morphemic level, where the representation of the sentence has the shape of a string rather than a tree.