The thermal runaway phenomenon in Ag/Bi 2 Sr 2 CaCu 2 O 8 composite conductors is studied for the nonlinear temperature and magnetic field dependences of their critical current density J c (T , B) and matrix resistivity ρ m (T , B) (nonlinear approximation). The influence of the applied magnetic field, heat transfer coefficient, matrix resistivity and volume fraction of the composite superconductor on the static thermal and electric states were investigated. The used model is based on steady heat and current balance equations. It allows us to investigate the non-isothermal voltage-current characteristic of composite superconductors, that roots the static description of their operating regimes and allows us to determine the limiting quantities of the thermal runaway parameters. It is found that there exist stable jumps of the electric field, current and temperature without the transition of the superconducting composite into the normal state. The presence of these static states is a result of the additional stable branches on the voltage-current characteristics, which appear according to the variation of the differential resistivity of a composite. The latter may have wide range fields due to the coupled thermo-magnetic and current-sharing mechanisms changing the quantities ∂ J c /∂ T and ∂ρ m /∂ T . This variation takes place when the applied magnetic field or operating parameters of a composite exceed some characteristic values. As a result, the non-monotonic temperature dependence of the Joule heat release will take place. Besides, it is shown that the stable voltage (without thermal runaway) may exist when the temperature of the Ag/Bi 2 Sr 2 CaCu 2 O 8 composite stably increases from the coolant temperature up to the critical temperature of a superconductor during current charging. The thermal runaway parameters as a function of the applied magnetic field are numerically derived accounting for the additional stable branches of the voltage-current characteristic.