Abstract: A pump for a free-flowing, in particular pasty or liquid, substance includes a support part, a pump element which has an elastically deformable membrane and can be pressed against the support part in opposition to a restoring force, and a pump chamber, disposed between the pump element and the support part, fluidly connected to an inlet valve and to an outlet aperture by an outlet valve, the outlet aperture passing through the membrane. On a side of the membrance which faces the pump chamber, a disk is provided, the disk together with the membrane forming the outlet valve, the disk being connected to the membrane so that in a closed position the membrane rests against the disk in an area enclosing the outlet aperture, and so that in an open position the membrane is arched upward partly away from the disk by a pressure exerted on it by the free-flowing substance, thereby forming an open connection between the outlet aperture and the pump chamber.