Duplex heat exchanger tubes consist of two concentric cylinders assembled in a state of prestress by shrink fitting. During operation, thermal expansion changes the interface pressure and this can cause a substantial increase in the thermal resistance of the tube. Under certain circumstances, more than one steadystate solution can be obtained. In this paper, the effect of this mechanism on the axial temperature variation in parallel or counterflow heat exchangers is analyzed. A method is developed for integrating the controlling equations for an arbitrary, non-linear, pressure-dependent contact resistance without iteration and the effect ofprestress and other parameters on the occurrence of in ultiple solutions is discussed.