Abstract: A control device for on the fly printing machines, especially machines for franking envelopes, comprises a printing device comprising a rotary print head actuated by a first motor and carrying on a portion of its surface a printing active part. A conveyor device for conveying the envelopes is actuated by a second motor and feeds the envelopes into contact with the printing device at a given conveyor speed and evacuates franked envelopes. The rotation speed of the first motor is optimized so that the tangential speed of the print head is held equal to the conveyor speed during a printing phase corresponding to the period during which an envelope is in contact with the active printing part and as close as possible to the conveyor speed during a complementary catch-up phase. The conveyor speed is optimized so that the conveyor speed is as low as possible whilst preventing overlapping of envelopes arriving on the conveyor device.