Combing machine for a cotton-fiber spinning preparation line, comprising at least two combing heads, wherein each combing head comprises: - a gripper and a circular comb, suitable for combing a fiber web; - at least one pair of detaching cylinders (20a', 20b'), downstream of the gripper, provided with unidirectional rotary motion; - a drafting device, located downstream of the gripper and of the detaching cylinders (20a', 20b'), suitable for drafting the combed web; wherein the drafting device comprises a first pair of drafting cylinders (602a, 602b) kept under pressure along an upstream gripping line (P') and a second pair of drafting cylinders (620a, 620b), downstream of the first pair, in pressure contact along a downstream pressure line (P"); characterized in that each combing head comprises deviation means, arranged downstream of the gripper and of the detaching cylinders (20a', 20b'), suitable for deflecting a sliver, wherein the combed web is condensed, towards a transverse direction of common advancement, along which the slivers of the combing heads are placed mutually side by side; and in that the drafting device is located upstream of the deviation means and comprises pressure means suitable for pressing the web of overlaid tufts between the upstream gripping line (P') and the downstream gripping line (P"); and the pressure means comprise: - an upper drafting belt, engaged with the first upper drafting cylinder and with a deflector element, for example a roller; and - a lower drafting belt, engaged with the first lower drafting cylinder and with a further deflector element, for example a baffle; wherein said belts (604a, 604b) run along respective closed paths and are in contact with each other along a contact section downstream of the upstream gripping line (P'). - a gripper and a circular comb, suitable for combing a fiber web; - at least one pair of detaching cylinders (20a', 20b'), downstream of the gripper, provided with unidirectional rotary motion; - a drafting device, located downstream of the gripper and of the detaching cylinders (20a', 20b'), suitable for drafting the combed web; wherein the drafting device comprises a first pair of drafting cylinders (602a, 602b) kept under pressure along an upstream gripping line (P') and a second pair of drafting cylinders (620a, 620b), downstream of the first pair, in pressure contact along a downstream pressure line (P"); characterized in that each combing head comprises deviation means, arranged downstream of the gripper and of the detaching cylinders (20a', 20b'), suitable for deflecting a sliver, wherein the combed web is condensed, towards a transverse direction of common advancement, along which the slivers of the combing heads are placed mutually side by side; and in that the drafting device is located upstream of the deviation means and comprises pressure means suitable for pressing the web of overlaid tufts between the upstream gripping line (P') and the downstream gripping line (P"); and the pressure means comprise: - an upper drafting belt, engaged with the first upper drafting cylinder and with a deflector element, for example a roller; and - a lower drafting belt, engaged with the first lower drafting cylinder and with a further deflector element, for example a baffle; - an upper drafting belt, engaged with the first upper drafting cylinder and with a deflector element, for example a roller; and - a lower drafting belt, engaged with the first lower drafting cylinder and with a further deflector element, for example a baffle; wherein said belts (604a, 604b) run along respective closed paths and are in contact with each other along a contact section downstream of the upstream gripping line (P').