We study germs of J-Holomorphic curves contained in M, a real analytic hypersurface of an symplectic manifold of dimension 4- We show, under topological hypothesis on M, that if M is compact then M is of finite type and so there is no germs of J-holomorphic curves on M (with J adapted with the symplectic form). In C2 with the standard complex structure, this is a classical result of Diederich-Fornaess.