A dispenser for holding multiple doses of fluids or other substances, and for dispensing the substances, has a vial, a flexible bladder received within the vial, and a variable volume storage chamber formed between the bladder and vial. A filling valve is coupled in fluid communication with the storage chamber and defines (1) a normally closed, fluid-tight position hermetically sealing the storage chamber from the ambient atmosphere, and (2) an open position allowing the passage of fluid through the valve both to evacuate the storage chamber and to introduce fluid through the valve to fill the storage chamber. A pump is coupled in fluid communication with the storage chamber for pumping fluids out of the storage chamber. A dispensing valve is coupled in fluid communication with the pump and defines (1) a normally closed, fluid-tight position preventing the passage of fluid out of the dispenser, and (2) an open position for dispensing pumped fluid therethrough. The sealed, empty dispenser is sterilized, such as by applying gamma radiation thereto. Then, the sterilized, sealed, empty dispenser is filled with fluid by engaging the filling valve with an evacuating/dispensing member to evacuate the storage chamber, and by introducing fluid from the filling member through the open filling valve and into the storage chamber. The filling member is withdrawn from the valve, and a spring moves the valve to a closed position to hermetically seal the fluid within the dispenser.