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More than one steady-state solution is shown to exist for the problem of steady-state heat transfer across the walls of a duplex tube when the initial prestress between the inner and outer tubes is sufficiently low. This determination was used in explaining the apparently erratic heat-transfer performance of prestressed duplex tubes in the steam generating system of the Experimental Breeder Reactor II. The importance of the results lies not only in showing that nonuniqueness of steady-state solution applies to more complex geometries than heretofore analyzed, but also in demonstrating that such multiple steady-state conditions appear in practical situations.