We give an analytic proof of the fractional monodromy theorem for the 1:-2 oscillator system with S^1 symmetry formulated by N. N. Nekhoroshev, D. A. Sadovskií, and B. I. Zhilinskií in C. R. Acad. Sci. Paris, Ser. I, 335 (2002) 985–988. Our proof is based on an analytic description of the Hamiltonian flow on the fibers of the integral map of this system.