The ABCD law for the complex parameter q of the TEM00 Gaussian beam is generally not valid for high-order modes. It can be used for the high-order modes or their superposition when the spot size w in the virtual part of the parameter q is substituted by the Rayleigh range ZR of a certain resonator. The focus characteristics of long distance flying optics are studied in this paper theoretically and experimentally for the TEMmn Gaussian beams between the two types of resonators without and with distortion. It is very important for the applications of the flying optical processing, the laser space craft and the spatial filter in the large laser project.