A theoretical and experimental investigation on thermal runaway phenomena of composite superconductors has been performed. It has been theoretically found that there are two substrate limited currents, a “thermal runaway current” Ih and a “completely stable current” Is, in addition to the take-off current and the recovery current. For a current above Ih the temperature of a composite conductor rises rapidly, and for a current below Is the conductor always recovers to superconducting state no matter how large a disturbance has occurred. The thermal runaway phenomena can be explained by considering the temperature dependences the resistivity of the substrate and heat transfer rate to liquid helium.The cornposite comductor tested consists of a copper strip 0.86mm thick by 2.16mm wide on which a copper-clad Ti-Nb-Ta superconducting wire of 0.37mm diameter (core dia.: 0.25mm) is soldered. The test results for the thermal runaway currents agreed well with the predicted. For example, the conductor in an external magnetic field of 43kOe began to runaway thermally at Ih=360A when the temperature reached about 30K. The teermal runaway current may be used as an important standard for designing a metastable superconducting coil.