Abstract: The invention generally concerns a submersible well pumping system comprising an axially elongated housing having a diameter less than the bore hole of the well, a multi-chamber hydraulically driven diaphragm pump, suspended in the well using coiled tubing, in which the coiled tubing contains one or more electrical cables to provide power to the pump from the surface. The pump is driven by a self-contained, closed loop hydraulic system, activated by an electric or hydraulic motor. The flow of working fluid into and out of the pumping chambers is controlled by a two state snap-acting valve, in turn controlled by a sensor which senses the proximity of the working diaphragm and generates an electrical signal to change the state of the valve, typically when either diaphragm reaches the bottom of the pumping stroke.