MONODROMY, DIABOLIC POINTS, AND ANGULAR MOMENTUM COUPLING D. A. Sadovski\'{\i} and B. I. Zhilinski\'{\i} Universit\'e du Littoral, BP 5526, 59379 Dunkerque Cedex, France communicated by P. R. Holland received 18.01.99 ms Ho 2693, Elsevier Science ref. PLA 8907, revised 12/98 accepted 06.04.99 Monodromy, or the most basic obstruction to global action-angle coordinates is shown to be present in the well known problem of two coupled angular momenta. It is also shown that in the corresponding quantum problem monodromy manifests itself as the redistribution of energy levels between different multiplets of the quantum spectrum. PACS: 03.20.+i; 03.65.Sq; 33.20Vq; 33.20Wr Keywords: Singular reduction; Orbit space; Energy-momentum map; Angular momentum coupling Physics Letters 256(4), 235-44 (1999)