Let Λ be a k-algebra of finite global dimension. We study tubular families in the Auslander–Reiten quiver of the bounded derived category D b (Λ) satisfying certain natural axioms. In particular, we precisely describe their influence on the cyclotomic factors of the Coxeter polynomial χ Λ of Λ and discuss several numerical limitations for their possible shapes. Moreover, we show that our results provide an alternative, relatively simple proof of non-trivial classical facts concerning tubular families in module categories, and also extend them slightly.