Let k be a positive integer, \(\{f_{n}(z)\}\) be a family of functions meromorphic on a domain D, whose zeros all have multiplicity at least k + 2, and let \(h(z)(\not \equiv 0)\) be a function holomorphic on D. Suppose \(f^{(k)}_{n}(z)\ne h(z)\) on D, and no subsequence of \(\{f_{n}\}\) is normal at some \(z_{0}\in D\). In this paper, we prove that the limit function \(f^{(k)}(z)\) of \(\{f^{(k)}_{n}(z)\}\) is equal to the exceptional function h(z) of derivatives \(f^{(k)}_{n}(z)\), and some characteristics of the subsequence of \(\{f_{n}(z)\}\) are obtained near the nor-normal point \(z_0\). As applications of this result, some quasinormal criteria are also given.

设k是一个正整数，\(\{f_{n}(z)\}\)是域D上的亚纯函数族，其零点都具有至少 k + 2 的重数，并令\(h( z)(\not \equiv 0)\)是D 上的全纯函数。假设\(f^{(k)}_{n}(z)\ne h(z)\)在D 上，并且\(\{f_{n}\}\)在某个\( z_{0}\in D\)。在本文中，我们证明了\(\{f^{(k)}_{n}(z)\}\)的极限函数\(f^{(k)}(z)\)等于导数的异常函数h ( z ) \(f^{(k)}_{n}(z)\)，以及\(\{f_{n}(z)\}\)的子序列的一些特征是在非正态点\(z_0\)附近获得的。作为该结果的应用，还给出了一些拟正规准则。