We study meromorphic functions in all ℂp or in a disc of ℂp. Using some properties of the valuation polygon notion, we show p-adic results perfectly analogous to those of Nevanlinna in the complex case. As an application we prove the p-adic analogue of Malmquist-Yosida Theorem: Let m∈ℕ and R(x.y)∈ℂp(x,y). If the differential equation: (dy/dx)=R(x,y), m∈ℕ, has a non rational meromorphic solution in all ℂp, then R(x,y) is a polynomial in y of degree ≤2m.