We shall discuss some questions related to the Birkhoff Normal Form of an analytic Hamiltonian system near a Diophantine equilibrium. This is classical subject but several questions still remain open. We shall in particular report on a recent work (joint with B. Fayad and R. Krikorian) which is related to (but does not solve) a question raised by M. Herman in his ICM lecture in Berlin 1996: is such an equi-librium always