Results on the motion of double layers from numerical simulations are presented. It was observed that after their formation double layers move toward the high-potential side. In simulations with sufficiently long plasmas, the moving double layer was found to occur along with a series of other plasma phenomena. These include electron beam plasma turbulence and resulting plasma heating, plasma evacuation, electron current and ion current interruptions and subsequent recoveries, and the acceleration of ''trapped'' ions on the low-potential side in an expanding plasma front moving with the double layer. Furthermore, we observed recurring formation and motion of double layers with the above plasma phenomena repeating periodically. In the largest simulated plasma of length d = 400 &ggr;D, where &ggr;D is the debye length at the low-potential end of the plasma, the double layers became supersonic with respect to the ion acoustic speed. The accelerated ''trapped'' ions moving with the double layer and the free ions accelerated by the double created counterstreaming ions on the low-potential side of the layer. The question of double layer motion in relation to current continuity across it is examined. The effect of ion current, injection on the double layer motion is simulated. The motion of double layers as seen in our simulations are compared with results from other simulations and those from laboratory experiments. The relevence of the simulation results to space plasma are qualitatively similar to those seen in the simulations.