  We find a method to rewrite the equations of motion of scalar fields,
generalized DBI field and quintessence, in the autonomous form
for\emph{arbitrary} scalar potentials. With the aid of this method, we explore
the cosmic evolution of generalized DBI field and quintessence with the
potential of multiple vacua. Then we find that the scalars are always frozen in
the false or true vacuum in the end. Compared to the evolution of quintessence,
the generalized DBI field has more times of oscillations around the vacuum of
the potential. The reason for this point is that, with the increasing of speed
$\dot{\phi}$, the friction term of generalized DBI field is greatly decreased.
Thus the generalized DBI field acquires more times of oscillations.
