In this work, we consider a Hamiltonian system with three degrees of freedom, whose linear part has all its roots pure imaginary and its three frequencies equal. We determine the Kernel of the Lie operator and the normal form, according to Meyer, of Hamiltonian in the diagonalizable case and in one of the nondiagonalizable cases, obtaining a normal form of the type obtained by Sokol s kii and Mansilla in previous works