| In this paper we mainly prove the following result:Let F and G be two families of functions meromorphic on a domain D (?) C, all of whose zeros have multiplicity at least k;. Let h (h≥0) be a constant and a is a finite complex number (|a|>h), for every f∈F and every g∈g, we have f(z)=0=(?)|f(k)(z)|≤h,g(z)=0(?)|g(k)(z)|≤h. Assume also that g is normal on D, and for any subsequence{gn} of g, gn=>9, we have g(?)∞and g(k)(?)α on D. If for every f∈F, there exists p∈g such that... |