I will apply an abstract Birkhoff normal form theorem in infinite dimension recently obtained by D. Bambusi and I (and presented in the talk by D. Bambusi) to concrete examples of Hamiltonian PDEs. These concrete examples include the NLW equation and the NLS equation in one space dimension with Dirichlet or Periodic boundary conditions. In particular, in the Dirichlet case, one gets that any small amplitude solution remains close to a torus for very long times. In the periodic case, resonances may appear and the result is more complicated; nevertheless, one gets a long time estimate of higher sobolev norms of the solution. Our results also applies to a particular NLS equation in higher dimension (with a convolution potential). I will focus on the verification of the hypothesis of the abstract theorem, in particular the nonresonances condition.