  The low energy dynamics of the vortices of the Abelian Chern-Simons-Higgs
system is investigated from the adiabatic approach. The difficulties involved
in treating the field evolution as motion on the moduli space in this system
are shown. Another two generalized Abelian Higgs systems are discusssed with
respect to their vortex dynamics at the adiabatic limit. The method works well
and we find bound states in the first model and scattering at right angles in
the second system.
