We present self-induced motion of salt-rich or Dextran-rich droplets in a PEG-rich aqueous phase when the droplets contain di(2-ethylhexyl) phosphate. The motion is produced by self-organized flow around the droplets. For the case of a single droplet random motion appears, whereas for multiple droplet systems symmetry of flow around the droplets is broken, and then a group of the droplets is clustered in one place.