P. Tuyls, M. Van Canneyt, A. Verbeure Anomalous Angular Momentum Fluctuations for an Ideal Bose Gas in a Rotating Bucket. (17K, LaTeX) ABSTRACT. An equilibrium superfluid is usually modelled by a Bose gas below its transition temperature. Here we compute rigorously the deviation from normality of the angular momentum fluctuations, and prove that the extremal phases, or the extremal equilibrium state components, show normal behaviour, except for special boundary conditions.