In a process for assembling two glass sheets (11, 12) to form an insulating glass pane, the glass sheets (11, 12) are arranged mutually parallel at a predetermined distance apart by means of suction conveyors. While the two sheets of glass (11, 12) are maintained at the predetermined distance apart by suction applied to their non-facing surfaces, without the use of any kind of spacers between them, an endless billet of an initially paste-like material which subsequently sets is injected along the edges and between the two sheets (11, 12), to which it adheres. During this time, the glass sheets are rotated synchronously, without any relative motion occurring between them, about an axis passing through their surfaces. Suction on one glass sheet (11) is then stopped and the insulating glass pane is transported and delivered by means of continued suction on the other glass sheet (12).