  We develop velocity-dependent models describing the evolution of string
networks that involve several types of interacting strings, each with a
different tension. These incorporate the formation of Y-type junctions with
links stretching between colliding strings, while always ensuring energy
conservation. These models can be used to describe network evolution for
non-abelian strings as well as cosmic superstrings. The application to $Z_{N}$
strings in which interactions are topologically constrained, demonstrates that
a scaling regime is generally reached which involves a hierarchy of string
densities with the lightest most abundant. We also study hybrid networks of
cosmic superstrings, where energetic considerations are more important in
determining interaction outcomes. We again find that networks tend towards
scaling, with the three lightest network components being dominant and having
comparable number densities, while the heavier string states are suppressed. A
more quantitative analysis depends on the precise calculation of the string
interaction matrix using the underlying string or field theory. Nevertheless,
these results provide further evidence that the presence of junctions in a
string network does not obstruct scaling.
