Various methods of approximating the kinetics of circulating fuel reactors are investigated. As the basis for comparison, a relatively “exact” model is used, predicated on perfect mixing in the core and slug flow in the external loop. The derivations and applicability of the various approximate methods are presented. It is shown that the frequency response of the “exact” model can exhibit peaking (i.e., resonances). The effect of such peaking on the transient response of the system is illustrated. The possibility of self-sustained oscillations of reactor power, resulting from the feedback caused by delayed neutron precursors re-entering the core, is also discussed.