  The Dirac method treatment for finite dimensional singular systems with
weakly vanishing Hamiltonian leads to obtain the equations of motion in terms
of parameter $\tau$. To obtain the correct equations of motion one should use
gauge fixing of the form $\tau - f(t)=0$. It is shown that the canonical method
leads to describe the evolution in both standard and constrained finite
dimensional systems with weakly vanishing Hamiltonian in terms of the physical
time $t$, without using any gauge fixing conditions. Besides the operator
quantization of the these systems is investigated using the canonical method
and it is shown that the evolution of the state $\Psi$ with the time $t$ is
described by the Schr/"odinger equation $i\frac{\partial \Psi}{\Partial t} =
{\hat H}\Psi$. The extension of this treatment to infinite dimensional systems
is given.
