Using a rather simple model of coupled, time-dependent Ginzburg-Landau
equations with two order parameters, we demonstrate that the total
Hamilitonian energy of the system contains at least three levels
describing point vortices, domain walls and configurations. The global
in time dynamics contain then also at least three different time
scales for nontrivial motions of domain walls, boundaries of domain
walls (frational degree vortices) and paired vortices. In particular,
we rigorously show, after an intial time period of adjusting, the
domain walls start to move according to motion by the mean-curvature
that straighten out the domain walls while the boundaries of such
domain walls are essentially fixed. After this motion is completed,
the fractional degree vortices begin to move at the next time scale.
The motion is relatively simple as it is of constant speed and toward
each other to form vortex pairs. Finally, these vortex pairs may move
in the final time scale very much like the ordinary vortices in a
single time-dependent Ginzburg-Laudau equation.