Abstract: It is consideredthat the abstraction problemfor generalized Hamiltonian affine control systems.In addition to the property of interest,the generalized Hamiltonian structure of the control system was pre-served and that howthe generalized Hamiltonian structure of control systems can be exploited to si mplify theabstraction process was shown.Then it is discussed these conditions under which local accessibility and con-trollability of the abstracted systemare equivalent to the corresponding properties of the original Hamiltoniancontrol system.