In the frame of magnetized plasmas, reconnection appears as an essential process for the description of plasma acceleration and changing magnetic field topology. Under the variety of reconnection regions in our solar system, we focus our research onto the Earth's magnetotail. Under certain conditions a Near Earth Neutral Line (NENL) is free to evolve in the current sheet of the magnetotail. Reconnection in this region leads to the formation of Earth- and tailward propagating plasma bulges, which can be detected by the Cluster or Geotail spacecraft. Observations give rise to the assumption that the evolved reconnection line does not provide a steady state behavior, but is propagating towards the tail (e.g., Baker et al., 2002). Based on a time-dependent variant of the Petschek model of magnetic reconnection, we present a method that includes an X-line motion and discuss the effects of such a motion. We focus our main interest on the shock structure and the magnetic field behavior, both for the switch-on and the switch-off phase.