In this paper, we discuss the normality of meromorphic functions which involves differential polynomial sharing values. We obtain two results: Let k be a positive integer, b (≠0) be a complex number, and be a polynomial with degree at least 2, and be a differential polynomial with . Let ℱ be a family of meromorphic functions defined in D, all of whose zeros have multiplicity at least . If has at least two distinct zeros, has at most one distinct zero in D for each , then ℱ is normal in D. If has at least two distinct zeros and for each pair of functions f and g in ℱ, and share b in D, then ℱ is normal in D, too. Two examples show that a condition in our results is necessary and our results improve Fang and Hong’s, and Zeng’s corresponding results.
MSC: Primary 30D35; secondary 34A05.