Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive clustertilted algebras. Moreover, we generalize Theorem 4.2 in [12] （Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc. 359（1）（2007）, 323-332.） to the situation of C Fm, and prove that the tilting graph KCFm of CFm is connected.
