The I-V characteristic of a superconductor is generally described by power-law,in which the superconductor with a high n transfers quickly from superconducting state to the normal conducting state.With a high transport current,in the low n value area,flux flow voltage becomes lower than in the high n value area,so that the transient characteristics strongly affect its stability.Based on those properties,we propose a new hybrid conductor which is made of low temperature superconductor(LTS) and high temperature superconductor(HTS) with concentric configuration in which the HTS coat is located outside of the LTS core.According to their power-law models,the modified adiabatic and dynamic stability criteria are qualitatively obtained by taking account into not only their critical currents but also n values.As a result,the new hybrid conductors have potential applications with higher engineering current density and improved stability. The IV characteristic of a superconductor is generally described by power-law, in which the superconductor with a high n transfers quickly from superconducting state to the normal conducting state. With a high transport current, in the low n value area, the flux flow voltage becomes lower than in the high n value area, so that the transient behavior strongly affect its stability. Based on those properties, we propose a new hybrid conductor which is made of low temperature superconductor (LTS) and high temperature superconductor (HTS) with concentric configuration in which the HTS coat is located outside of the LTS core. Accredited to their power-law models, the modified adiabatic and dynamic stability criteria are qualitatively obtained by taking account into not only their critical but also n values. As a result, the new hybrid conductors have potential applications with higher engineering current density and improved stability.