Cutting unit S for agricultural machines, in particular balers P or loading wagons, comprising: a rotor adapted to rotate in a direction of rotation about an axis having an at least substantially cylindrical base body carrying tine arrangements (6, Z), the tine arrangements (6, Z) being parallel to each other in planes perpendicular to the axis and distributed in the direction of the axis of the base body with intermediate distances in between, each tine arrangement (6, Z), including at least one tine consisting of a base secured to the base body and at least one outwardly protruding, substantially triangular tine tip, the tine tip having a conveying flank leading in the direction of rotation of the rotor and extending from an outer tine end to a transition into the base, the base of the tine having a base section at the leading side of the tine and a trailing base section, the base being provided with an outwardly facing compression surface gradually ascending opposite to the direction of rotation to the transition into the conveying flank a cutting unit bottom distant from the rotor forming a lower boundary of a conveying channel through the cutting unit, cutting blades protruding from the cutting unit bottom through the conveying channel besides moving paths of the tine tips, cutting edges of the cutting blades being oriented counter to a conveying direction in the conveying channel as defined by the direction of rotation of the rotor, and scrapers placed in conveying direction behind the rotor, the scrapers extending in between the tine arrangements (6, Z) close to a periphery of the base body, characterized in that the compression surface is convexly curved and gradually ascends from a starting point at least along an outer contour of the base section up to the transition into the conveying flank and extends at each tine over an angular range (β) of the tine arrangement (6, Z) of about 60° to about 100°. a rotor adapted to rotate in a direction of rotation about an axis having an at least substantially cylindrical base body carrying tine arrangements (6, Z), the tine arrangements (6, Z) being parallel to each other in planes perpendicular to the axis and distributed in the direction of the axis of the base body with intermediate distances in between, each tine arrangement (6, Z), including at least one tine consisting of a base secured to the base body and at least one outwardly protruding, substantially triangular tine tip, the tine tip having a conveying flank leading in the direction of rotation of the rotor and extending from an outer tine end to a transition into the base, the base of the tine having a base section at the leading side of the tine and a trailing base section, the base being provided with an outwardly facing compression surface gradually ascending opposite to the direction of rotation to the transition into the conveying flank a cutting unit bottom distant from the rotor forming a lower boundary of a conveying channel through the cutting unit, cutting blades protruding from the cutting unit bottom through the conveying channel besides moving paths of the tine tips, cutting edges of the cutting blades being oriented counter to a conveying direction in the conveying channel as defined by the direction of rotation of the rotor, and scrapers placed in conveying direction behind the rotor, the scrapers extending in between the tine arrangements (6, Z) close to a periphery of the base body, characterized in that the compression surface is convexly curved and gradually ascends from a starting point at least along an outer contour of the base section up to the transition into the conveying flank and extends at each tine over an angular range (β) of the tine arrangement (6, Z) of about 60° to about 100°. a cutting unit bottom distant from the rotor forming a lower boundary of a conveying channel through the cutting unit, cutting blades protruding from the cutting unit bottom through the conveying channel besides moving paths of the tine tips, cutting edges of the cutting blades being oriented counter to a conveying direction in the conveying channel as defined by the direction of rotation of the rotor, and scrapers placed in conveying direction behind the rotor, the scrapers extending in between the tine arrangements (6, Z) close to a periphery of the base body, the compression surface is convexly curved and gradually ascends from a starting point at least along an outer contour of the base section up to the transition into the conveying flank and extends at each tine over an angular range (β) of the tine arrangement (6, Z) of about 60° to about 100°.