A connection device and process connect a patient-side coupling unit to a source/sink of a gas including oxygen. The connection device includes a valve device with a first valve (40.1) and with a second valve (40.2). A source-side fluid guide unit establishes a fluid connection between the source or the sink and the valve device. A patient-side fluid guide unit establishes a fluid connection between the patient-side coupling unit and the valve device. The valves are connected in parallel and are arranged between the two fluid guide units. A gas flows from the source through the first and/or second valve to the patient-side coupling unit or through the first and/or second valves to the sink. A control pressure is set at each valve. As a result, the time course of the volume flow downstream of the valve device follows a predefined time course.