A cranking harmonic oscillator model, widely used for the physics of fast rotating nuclei and Bose-Einstein condensates, is re-investigated in the context of PT -symmetry. The instability points of the model are identified as exceptional points. It is argued that -even though the Hamiltonian appears hermitian at first glance -it actually is not hermitian within the region of instability. PACS numbers: 03.65.Vf, 03.75.Kk, 02.40.Xx Quantum instabilities are attracting considerable attention in a variety of physical situations. They can be associated with the formation of solitons and vortices in Bose-Einstein condensates [1], with a sudden change of the moment of inertia of a rotating nucleus (see, for example, Ref.2 and references therein) and a transition from one-to two-dimensional nuclear rotation [3]. A particular example of interest is the Hamiltonian H = ω 1 (a † 1 a 1 +