  We show that nonuniform superconductors of the
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type conduct electric current in the
way which is very different from the usual case. We discuss both equilibrium
and nonequilibrium properties using a modified Ginzburg-Landau formalism. Among
the novel features are the existence of two different critical currents and two
distinct stable states able to carry a given current, the possibility of
superconducting domain walls, and also a spontaneous supercurrent in a ring
geometry.
