Let k be a positive integer and b a nonzero constant. Suppose that F is a family of meromorphic functions in a domain D. If each function f ∈ F has only zeros of multiplicity at least k + 2 and for any two functions f, g ∈ F, f and g share 0 in D and f(k) and g(k) share b in D, then F is normal in D. The case f ≠ 0, f(k) ≠ b is a celebrated result of Gu.