中文摘要：

利用亚纯函数值分布理论与正规理论的一些基本概念、研究方法以及研究成果,并以顾永兴的定理为基础,讨论函数族中任意函数的高阶零点不取固定函数的这类亚纯函数的正规问题,最后得到如下正规定则：设F是单位圆盘内的一族亚纯函数,k为一个正整数,且k≥2,A为一有穷正数,h（z）是全纯函数,其中h（z）≠0,如果对任意的f∈F,f的零点重级至少为k,且f的极点重级至少为3;并且满足当f（z）=0时,必有f（k）（z）≤A;f的k阶导数不取固定函数h（z）,即f（k）（z）≠h（z）,则F在区域内是正规的.

英文摘要：

By using some fundamental knowledge ,research methods and research results about the theories of value distribution and normal family for meromorphic functions and based on Gu＇ s theorem,a criterion of normality concerning meromorphic functions whose higher zeros are not fixed functions was provided,and is described as follows：let k≥2 be an integer and f be a family of meromorphic functions on a unit disc △, all the zeros of every f which belongs to f have multiplicity at least k and all the Doles have multiplicity at least 3, h （z） be a holomorphicfunctions,and h（z）≠O,and assume that the following two conditions that f（z） = 0===〉 ｜f（k）｜≤A, A is a positive number,and f（k）（z）≠h（z） hold for every f∈f,then Nis normal in A.