The stability of annular flow in a rotating heat pipe with a cylindrical wall is investigated. Critical conditions are established for the collapse of the annular liquid body; a first-order perturbation solution of the two-dimensional flow equations is presented. These criteria are applicable to viscous as well as inviscid annular flow, which corresponds to the limiting case of large Reynolds numbers. The theoretical results are compared with experimental data from visualization experiments, in which water is employed as the working fluid. A modification of a criterion for inviscid flow is made.