  Networks or webs of domain walls are admitted in Abelian or non-Abelian gauge
theory coupled to fundamental Higgs fields with complex masses. We examine the
dynamics of the domain wall loops by using the moduli approximation and find a
phase rotation induces a repulsive force which can be understood as a Noether
charge of Q-solitons. Non-Abelian gauge theory allows different types of loops
which can be deformed to each other by changing a modulus. This admits the
moduli geometry like a sandglass made by gluing the tips of the two
cigar-(cone-)like metrics of a single triangle loop. We conclude that the sizes
of all loops tend to grow for a late time in general models with complex Higgs
masses, while the sizes are stabilized at some values once triplet masses are
introduced for the Higgs fields. We also show that the stationary motion on the
moduli space of the domain wall webs represents 1/4 BPS Q-webs of walls.
