The present invention pertains to the object of substantially increasing the performance of an envelope-stuffing machine. While EP-A-0 504 114 discloses the use of rotating elements for opening the envelopes and for grasping the envelope flaps for this purpose, the present invention suggests that the opening and grasping of the envelopes (20) be performed in one conveying plane (13), and the introduction of the envelope contents (21) be performed in a conveying plane (12) arranged offset in relation thereto at another level, and that a link chain (10) with a plurality of spreading members (9) be provided between them, which is movable at right angles to the conveying planes (12, 13) and keeps the envelopes (20) picked up by the spreading members (9) ready at another point for the introduction of the envelope contents (21) and discharges them.