To perform automatic work for connecting two laps of one being an preceding lap and the other being a succeeding lap by mounting a device, having comparatively simple constitution, on a comber machine.

Only the rear pack lap roller 2 of a pair of rollers 1 and 2 on which a small lap roll ER is placed is moved to the rear of a machine bed. After a preceding lap OL is cut between a pair of grasping rollers 9, 11 and the front lap roller 1, the back lap roller 2 is moved further rearward and the small lap roll ER is discharged. With this state, the succeeding lap NL of a full lap roll FR newly placed on a pair of lap rollers 1 and 2 is fed onto a lap conductor 8. The preceding and succeeding laps NL and OL are lapped together on the lap conductor 8 and a pusher 43 is forced into pressure contact with the lapped part and the succeeding and the preceding laps NL and OL are automatically interconnected.