The nth order wave interaction theory investigated in this paper should be considered as a continuation of the "exact solution to solitary wave equations of light interaction with two-level atomic systems" in the earlier paper[1]. In literature[4,5] the third order wave equations originate from the research of three-wave interaction. But the nth order wave equations considered now are derived from the w-dimensionall vector functions which satisfy two nonlinear equations, and the general solutions can be expressed in terms of the upper hemiplane analytical solutions and the lower hemiplane analytical solutions. These results include the 2nd and the 3rd order solutions as a special example.