A new method of multiple scales procedure is used to analyze the forced responses of multiple degrees of freedom systems with cubic non-linearity, in which the internal resonance takes place simultaneously together with the forced resonances. Attention is focused on the superharmonic and subharmonic resonance caused by internal resonance as Ω is near Ω 1or Ω 2, where Ω is the forcing frequency, and Ω 1and Ω 2 are the first and the second natural frequencies. It is found that the responses are usually excitation-level dependent and there is a critical excitation amplitude ƒ c. In the case of Ω near Ω 1, when ƒ>ƒ c the "out-of-phase" superharmonic resonance disappears. In the case of Ω near Ω 2, when 0<ƒ<ƒ c, there are two branches of response; when ƒ>ƒ c, one branch of responses vanishes. The critical excitation amplitudes in different forced vibration are determined analytically in this paper.