Nonlinear equation for atmospheric gravity waves is derived and nonlinear behavious of the waves are studied.Nonlinear ionospheric response to atmospheric gravity waves is also studied.The structures of nonlinear TIDs are presented.The nonlinear effects cause waveform distortion of TIDs.The disturted TIDs appear to be "sharp peaked" shapes and "sawtooth" shapes.The nonlinear theory of TIDs preserited in this paper can describe ionospheric irregularities and shows a good agreement with various observations on TIDs.