  In the framework of started in Ref.[1] construction procedure of the general
superfield quantization method for gauge theories in Lagrangian formalism the
rules for Hamiltonian formulation of general superfield theory of fields (GSTF)
are introduced and are on the whole considered.
  Mathematical means developed in [1] for Lagrangian formulation of GSTF are
extended to use in Hamiltonian one. Hamiltonization for Lagrangian formulation
of GSTF via Legendre transform of superfunction $S_{L}\bigl({\cal
A}(\theta),{\stackrel{\circ}{\cal A}}(\theta),\theta\bigr)$ with respect to
${\stackrel{\circ}{{\cal A}^{\imath}}}(\theta)$ is considered. As result on the
space $T^{\ast}_{odd}{\cal M}_{cl}\times \{\theta\}$ parametrized by classical
superfields ${\cal A}^{\imath}(\theta)$, superantifields ${\cal
A}^{\ast}_{\imath}(\theta)$ and odd Grassmann variable $\theta$ the
superfunction $S_{H}({\cal A}(\theta),{\cal A}^{\ast}(\theta),\theta)$ is
defined. Being equivalent to different types of Euler-Lagrange equations the
distinct Hamiltonian systems are investigated. Translations along $\theta$ for
superfunctions on $T^{\ast}_{odd}{\cal M}_{cl}\times \{\theta\}$ being
associated with these systems are studied. Various types of antibrackets and
differential operators acting on $C^{k}\bigl(T^{\ast}_{odd}{\cal M}_{cl} \times
\{\theta\} \bigr)$ are considered. Component (on $\theta$)formulation for GSTF
quantities and operations is produced. Analogy between ordinary Hamiltonian
classical mechanics and GSTF in Hamiltonian formulation is proposed.
Realization of the GSTF general scheme is demonstrated on 6 models.
