A self-inflating tire assembly includes an air passageway in the tire that is operable to be sequentially flattened by the tire footprint in a direction opposite to a tire direction of rotation to pump air from an inlet device through the passageway to an outlet device for direction into the tire cavity. A valve device for a tire is also disclosed. The valve device includes an insert mounted in the tire, a valve body mounted within the valve insert; wherein the valve body has a first, second and third chamber, wherein a first and second check valve is positioned in the first and second chamber. A pressure membrane is received within the valve body, and positioned to open and close the third chamber. The pressure membrane is in fluid communication with the tire cavity and the third chamber of the valve body. A spring is received within the third chamber and is positioned to exert force upon the pressure membrane to bias the pressure membrane position relative to the channel in the open position.