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Centaurs are widely believed to come from the Edgeworth-Kuiper belt, located beyond the orbit of Neptune. From here they can be injected into the inner part of the Solar System through planetary perturbations or mutual collisions. Due to their origin and dynamical evolution, Centaurs are supposed to constitute a transition population of objects from the large reservoir of Trans-Neptunian Objects (TNOs) to the active bodies of the inner Solar System. On the basis of the present knowledge of the physical properties of Centaurs and TNOs a similarity between the two populations appears evident. This is the strongest observational constraint supporting the theory of common origin.