Constant-velocity pivot joint for torque transmission, comprising: a joint outer part having a plurality of outer ball tracks (20a; 20b), a joint inner part having a plurality of inner ball tracks (40a; 40b), torque-transmitting balls (30; 31) which are each guided in track pairs of outer ball tracks (20a; 20b) and inner ball tracks (40a; 40b), and a cage which receives the balls (30; 31) in circumferentially distributed cage windows and holds them in a common joint centre plane when the constant-velocity pivot joint is in a straight line, wherein the joint outer part has a longitudinal axis (La) and, situated axially opposite one another, an opening side and a connection part, and the path of the centre points of the balls (30; 31) is in each case defined as a centre line (MS; MN) of the respective ball track, and characterized in that a first type of track pairs of ball tracks (20a; 40a) is designed in such a way that centres of curvature of the centre lines of the ball tracks lie in the joint centre plane when the joint is in a straight line, while a second type of track pairs of ball tracks (20b; 40b) is designed in such a way that their centre lines have at least two portions (MSi; MSa), and the respective centre line of the outer ball tracks of the second type of track pairs has at least one inner portion (MSi) and one outer portion (MSa), wherein the inner portion (MSi) lies on the connection side of the joint outer part, while the outer portion (MSa) lies on the opening side of the joint outer part, and the inner portion (MSi) is curved and the centre of curvature (OT') of the inner portion (MSi) lies within the hollow volume of the joint outer part with an offset from the joint centre plane towards the opening side when the joint is in a straight line, while the centre line flares out through the outer portion (MSa) towards the opening side. a joint outer part having a plurality of outer ball tracks (20a; 20b), a joint inner part having a plurality of inner ball tracks (40a; 40b), torque-transmitting balls (30; 31) which are each guided in track pairs of outer ball tracks (20a; 20b) and inner ball tracks (40a; 40b), and a cage which receives the balls (30; 31) in circumferentially distributed cage windows and holds them in a common joint centre plane when the constant-velocity pivot joint is in a straight line, wherein the joint outer part has a longitudinal axis (La) and, situated axially opposite one another, an opening side and a connection part, and the path of the centre points of the balls (30; 31) is in each case defined as a centre line (MS; MN) of the respective ball track, and characterized in that a first type of track pairs of ball tracks (20a; 40a) is designed in such a way that centres of curvature of the centre lines of the ball tracks lie in the joint centre plane when the joint is in a straight line, while a second type of track pairs of ball tracks (20b; 40b) is designed in such a way that their centre lines have at least two portions (MSi; MSa), and the respective centre line of the outer ball tracks of the second type of track pairs has at least one inner portion (MSi) and one outer portion (MSa), wherein the inner portion (MSi) lies on the connection side of the joint outer part, while the outer portion (MSa) lies on the opening side of the joint outer part, and the inner portion (MSi) is curved and the centre of curvature (OT') of the inner portion (MSi) lies within the hollow volume of the joint outer part with an offset from the joint centre plane towards the opening side when the joint is in a straight line, while the centre line flares out through the outer portion (MSa) towards the opening side.