In the last step of the induction used in the proof of his uniformisation theorem of Haken manifolds, Thurston stated « boundedness theorem ». It turned out that a weaker version of this theorem is sufficient for the proof of the uniformisation theorem, and no full proof of the original boundedness theorem has been given up to now. We shall give its proof relying on recent progress of Kleinian group theory. This is joint work with Cyril Lecuire.