The laterally nonlinear vibration of axially moving beams weve analyzed by the incremental harmonic balance(IHB) method.Firstly the motion equations of an axially moving beam weve derived by Hamilton's principle,Then the Galerkin method was used to discretize the governing equations.Finally, the IHB method was employed to solve the nonlinear vibration equations.Particular attention was paid to the fundamental,subharmonic resonance with internal resonance under the condition ω20/ω10≈3 as ω is near ω20,ω10,where ω is the forcing frequency,and ω10 and ω20 are the first and the second natural frequencies.The number results show that the IHB method is a very effective semi-analytical and seminumerical method for nonlinear vibration of axially moving system.