Abstract: An apparatus for degassing a liquid or pasty medium in a machine for producing and/or upgrading a fiber material web includes a vessel rotatable about an axis of rotation, a medium-supply device for introducing the medium to be degassed into the vessel, a medium-discharge device for discharging a low-gas fraction of the medium out of the vessel and a gas-discharge device for discharging a gas-rich fraction of the medium out of the vessel. The gas-discharge device has an immersion-tube arrangement with at least one immersion tube, the inlet orifice of each being arranged so as to be at least adjacent to the axis of rotation of the vessel.