The instability associated with the onset of motion in a toroidal natural-circulation loop has been studied theoretically. A one-dimensional model is used to investigate the problem of global flow initiation from a rest state. It is shown that a thermosyphonic flow is established when the modified Rayleigh number exceeds a critical value, Rc* or Rc, which depends on the modified Biot number B. For a loop heated by a uniform heat flux Rc* is between the limits of 1/4 and 2.816 for small and large B, respectively. For a loop heated by a prescribed constant wall temperature, Rc has a minimal value of 2 at B=1. These results were obtained by two methods: a direct solution of the steady-state problem and a stability analysis of the rest state. The latter shows that when R*>Rc* there is a single monotonously growing perturbation and there are always additional monotonously decaying disturbance modes.