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The stability of He-II-cooled multilayer magnets usually is limited because of the finite amount of helium close to each conductor, For such cases, the heat flux at the conductor surface falls steadily with time following a normal zone initiation. For full cryogenic stability in large coils, such as magnetic energy storage magnets, the heat conduction capacity to He II should be larger than the I2R heat produced in a normal conductor on a continuous basis, providing recovery from large initial normalizing heat pulses. Using both finite element and finite difference techniques, the heat conduction equation for two-layer coils in He II is solved for both steady-state and transient conditions in two dimensions to yield the heat flux at the conductor surface and the total enthalpy absorbed by He II at any time. Two-layer coils are specified so that all conductors in each layer share a common bath of helium. Solutions are given for different normal-zone lengths at different positions in the coil. Heat fluxes at the surface of the conductor as high as 2.5 watt/cm2can be cooled for a long time (t>200 sec.).