  We study co-existence system of both bosonic and fermionic degrees of
freedom. For such system with up to first derivatives in Lagrangian, we find
Ostrogradsky-type ghost-free condition in Hamiltonian analysis, which is found
to be the same with requiring that the equations of motion of fermions are
first-order in Lagrangian formulation. When fermionic degrees of freedom are
present, uniqueness of time evolution is not guaranteed a priori because of the
Grassmann property. We confirm that the additional condition, which is
introduced to close Hamiltonian analysis, also ensures the uniqueness of the
time evolution of system.
