A method of pumping fluid including the steps of providing an electrokinetic pump comprising a pair of double-layer capacitive electrodes having a capacitance of at least 10.sup.-2 Farads/cm.sup.2 and being connectable to a power source, a porous dielectric material disposed between the electrodes and a reservoir containing pump fluid; connecting the electrodes to a power source; and moving pump fluid out of the reservoir substantially without the occurrence of Faradaic processes in the pump. The invention also includes an electrokinetic pump system having a pair of double-layer capacitive electrodes having a capacitance of at least 10.sup.-2 Farads/cm.sup.2; a porous dielectric material disposed between the electrodes; a reservoir containing pump fluid; and a power source connected to the electrodes; the electrodes, dielectric material and power source being adapted to move the pump fluid out of the reservoir substantially without the occurrence of Faradaic processes in the pump.