We investigate the evolution of a superconducting string network with
arbitrary, constant string current in the friction dominated regime. I
n the absence of an external magnetic field the network always reaches
a scaling solution. However, for string current stronger than a criti
cal value, it is different than the usual horizon scaling of the nonsu
perconducting string case. In this case the friction domination era ne
ver ends. Whilst the superconducting string network can be much denser
than usually assumed, it can never dominate the universe energy densi
ty. It can, however, influence the cosmic microwave background radiati
on and the formation of large scale structure. When embedded in a prim
ordial magnetic field of sufficient strength, the network never reache
s scaling and, thus, eventually dominates the universe evolution.