Tunneling barriers, in particular superconductive tunneling barriers (Josephson barriers), are prepared in a vacuum chamber maintained at a low atmospheric pressure using an oxygen glow discharge which produces stable and reproducible superconductive tunneling devices. To prepare a Pb-Pbx Oy-Pb barrier the first lead film is placed in a vacuum chamber and charged to a negative potential with regard to the positive ions by fast electrons from the plasma charge. Oxygen gas molecules bombard the first lead film where they probably disassociate into two oxygen atoms. A surface reaction takes place which produces a lead-oxide insulating layer in the first lead film. After this lead-oxide layer has reached a predetermined thickness, the plasma is extinguished and the oxygen-lead reaction stops. Immediately after the oxide formation, a second lead layer is evaporated onto the oxide layer to form a tunneling barrier of the Josephson type. Instead of forming a lead-oxide insulating layer into the first lead film, polymerized organic molecules may be formed on the lead surface by the high energy bombardment.