  Magnetic flux ropes in space are generally connected to some regions
electromagnetically. We consider the whole closed current system of the
expanding flux ropes including the electric current associated with them. By
combining the theories regarding the self-similar expansion of cylindrical flux
ropes and the Alfven wave current system, we examine conditions under which the
electric current matches. These matching conditions are satisfied when the time
dependence of the current flowing in the closed circuit agrees with that which
maintains the expanding flux rope. In consequence, we encountered three
possible forms of expansion. The two-step eruption of solar filaments may be
interpreted as a transition from one form of expansion to another. If this
process works, increasing the diffusion outside of the flux rope is necessary
to trigger the transition.
