Systems are described for delivery of a wide variety of materials in which liquid and gas or vapor states are concurrently present, from a package preferably including a fluid-containing collapsible liner. Headspace gas is removed from a pressure dispensing package prior to liquid dispensation therefrom, and ingress gas is removed thereafter during dispensation operation. At least one sensor senses presence of gas or a gas-liquid interface in a reservoir or gas-liquid separation region. A gas removal system including an integral reservoir, at least one sensor, and at least one flow control elements may be included within a connector adapted to mate with a pressure dispensing package, for highly efficient removal of gas from the liquid being dispensed from the container.