Abstract: In some engineering problems, thermo-mechanical coupling is important and may not be ignored. This paper deals with the crack propagation problem in a coupled thermo-mechanical system of nonlinear media. Various nonlinear media, including nonlinear e-lastic and elastic-plastic cases, have been considered and the related path-independent integrals are given. To explain the physical meaning of these integrals, a notched specimen has been considered, and the dynamical crack extension force in a coupled thermo-mechanical system is shown to be equal to this integral. Thus, we could consider such integrals as some nonlinear criteria for coupled thermo-mechanical fracture dynamics.