In this paper we proved the following theorems: Theorem 1 Let f(z) be a meromorphic function of infinite order ρ(r). Then there exists a ray B: argz=θ_0 (0≤θ_0<2π) such that if h, l, p, k arbitrary positive number and α(z), β(z) are two arbitrary meromorphic function satisfying lim logT(r,α)/ρ(r)logr<1, lim logT(r,β)/ρ(r)logr<1,and α^((k))(z)■β(z), then Theorem 2 Let f(z) be a meromorphic function of infinite order ρ(r). Then there exists a ray B: argz=θ_0(0≤θ_0<2π)such that if n is a positive integer satisfying n≥3, and if e is an arbitrary positive number, β(z) is an arbitrary meromorphic function satisfying lim logT(r,β)/ρ(r)logr<1, β(z)■0, then
