Let F(z,w) be a holomorphic function in CnĂC of finite order in w with nâ„2. Let Ω be the set of points zâCn where F(z,w) is a non-constant function omitting a value Ï(z). Near a finite accumulation point z0 of Ω, we prove in the main result (Theorem 1) that Ω is a local analytic set and Ï(z) is holomorphic, and show the existence of a proper globally analytic set Î of Cn such that either ΩâÎ or Ω=CnâÎ, being possible in the last case to also determine F(z,w) in terms of Ï(z). We apply this result to several problems. First, we extend a Theorem due to Nishino about exceptional values when near z0 dimension of Ω is n and assure the existence of a meromorphic function α(z) in Cn such that Ï(z)=α(z) except at points where α(z) has poles or F(z,w) is constant (also being F(z,w) a polynomial in w if α(z) is â). After, we prove that Ω is a local analytic set in Cn and the existence of a proper analytic subset E of Cn such that ΩâE or Ω=CnâE. Finally, we generalize a Lelong-Gruman Theorem about the set of points z where Ï(z)=0.