A device is provided to produce an embossed multi-ply material, comprising: a first embossing-laminating unit (3) comprising a first embossing cylinder (5) equipped with first projections (5P) defining a first pattern, a first pressure roller (7) cooperating with said first embossing cylinder (5), a first laminating roller (9) and a first glue dispenser (11), disposed between said first pressure roller (7) and said frst laminating roller (9); an embossing unit comprising at least a second embossing cylinder (25) provided with second projections (25P) defining a second pattern and a second pressure roller (27) cooperating with said second embossing cylinder (25); a first path (P1) through said first embossing-laminating unit (3); a second path (P2) for at least a second ply (V2) towards and through said second embossing unit (23); a third path (P3) for said third ply (V3).