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The nonideal semi-Gaussian beam generated in the experiment has a certain ascent border width.Due to its asymmetry,the propagation properties of a nonideal semi-Gaussian laser beam in the nonlinear materials have some of unique characters.In this paper,the propagation properties of a nonideal semi-Gaussian laser beam with a small ascent border width through the ZnSe nonlinear crystal has been theoretically studied,and the relations of the propagation properties and the various parameters of the nonlinear medium and the semi-Gaussian beams have been also analyzed theoretically in detail.