A critical power dissipation resulting from an oscillating magnetic field,Hpcos&ohgr;t, can produce a magnetic breakdown field,Hp′ <Hc, the critical field of the superconductor. The analysis shows, for example, why the breakdown field of a superconducting microwave cavity can be well belowHcin some cases, and indicates what the functional dependence of the cavityQmay be for values ofHpnearHp′. The effective resistivity of a single isolated oscillating fluxoid, as well as that of a stationary normal region, is also derived for both type I and type II superconductors.