In this paper, we provide a quantitative analysis of non-projective constructions attested in the Ancient Greek Dependency Treebank (AGDT). We consider the different types of formal constraints and metrics that have become standardized in the literature on non-projectivity (planarity, wellnestedness, gap-degree, edge-degree). We also discuss some of the linguistic factors that cause non-projective edges in Ancient Greek. Our results confirm the remarkable extension of non-projectivity in the AGDT, both in terms of quantitative incidence of non-projective nodes and for their complexity, which is not paralleled by the corpora of modern languages considered in the literature. At the same time, the usefulness of other constraint (especially well-nestedness) is confirmed by our researches. 1