Kit for producing a connection of a first composite pipe to a second pipe by means of a sleeve, the kit comprising the first composite pipe, wherein at least the first composite pipe is configured - with a smooth inner pipe, - with a corrugated outer pipe which has -- corrugation crests (3, 4) and -- corrugation troughs each located between corrugation crests (3, 4) directly adjacent to one another, which are bounded towards the inner pipe by corrugation feet connecting the corrugation crests (3, 4) to one another, the corrugation feet being welded to the inner pipe via the circumference of the composite pipe, - with large sidewall portions (15, 15') facing each other, of which one large sidewall portion is configured as to be curved outwardly, - with small sidewall portions (13, 13') connecting the large sidewall portions (15, 15') to each other, facing each other and being configured as to be curved outwardly, - with a small axis penetrating the large sidewall portions (15, 15'), the small sidewall portions (13, 13') being arranged mirror-symmetrically to the small axis, and - with a large axis penetrating the small sidewall portions (13, 13'), - wherein both large sidewall portions (15, 15') are configured as to be curved, are arranged mirror-symmetrically with respect to the large axis, and are configured symmetrically with respect to the small axis, respectively, characterized in - that the small sidewall portions (13, 13') and the large sidewall portions (15, 15') are each connected to one another by means of a transition portion (16, 16'), - that the kit comprises the sleeve, - that the sleeve has a first and a second sleeve portion (31, 31'), - that the sleeve portions (31, 31') have an insertion end each for the insertion of a spigot end (29, 29') of the first composite pipe and the second pipe, respectively, - that at least the first sleeve portion, in the region of the insertion end, has a first inner cross section which corresponds to the outer cross section of the spigot end of the first composite pipe plus a circumferential gap having a gap width d1, and - that at least the first sleeve portion, adjacent to an insertion region (stop 34), has a second inner cross-section which, with the outer cross-section of the spigot end of the first composite pipe, bounds the gap with a gap width d2 in the region of the large sidewall portions (15, 15') and a gap width d3 in the region of the small sidewall portions (13, 13'), where: d 1 > d 2 > d 3. - with a smooth inner pipe, - with a corrugated outer pipe which has -- corrugation crests (3, 4) and -- corrugation troughs each located between corrugation crests (3, 4) directly adjacent to one another, which are bounded towards the inner pipe by corrugation feet connecting the corrugation crests (3, 4) to one another, the corrugation feet being welded to the inner pipe via the circumference of the composite pipe, -- corrugation crests (3, 4) and -- corrugation troughs each located between corrugation crests (3, 4) directly adjacent to one another, which are bounded towards the inner pipe by corrugation feet connecting the corrugation crests (3, 4) to one another, the corrugation feet being welded to the inner pipe via the circumference of the composite pipe, - with large sidewall portions (15, 15') facing each other, of which one large sidewall portion is configured as to be curved outwardly, - with small sidewall portions (13, 13') connecting the large sidewall portions (15, 15') to each other, facing each other and being configured as to be curved outwardly, - with a small axis penetrating the large sidewall portions (15, 15'), the small sidewall portions (13, 13') being arranged mirror-symmetrically to the small axis, and - with a large axis penetrating the small sidewall portions (13, 13'), - wherein both large sidewall portions (15, 15') are configured as to be curved, are arranged mirror-symmetrically with respect to the large axis, and are configured symmetrically with respect to the small axis, respectively, characterized in - that the small sidewall portions (13, 13') and the large sidewall portions (15, 15') are each connected to one another by means of a transition portion (16, 16'), - that the kit comprises the sleeve, - that the sleeve has a first and a second sleeve portion (31, 31'), - that the sleeve portions (31, 31') have an insertion end each for the insertion of a spigot end (29, 29') of the first composite pipe and the second pipe, respectively, - that at least the first sleeve portion, in the region of the insertion end, has a first inner cross section which corresponds to the outer cross section of the spigot end of the first composite pipe plus a circumferential gap having a gap width d1, and - that at least the first sleeve portion, adjacent to an insertion region (stop 34), has a second inner cross-section which, with the outer cross-section of the spigot end of the first composite pipe, bounds the gap with a gap width d2 in the region of the large sidewall portions (15, 15') and a gap width d3 in the region of the small sidewall portions (13, 13'), where: d 1 > d 2 > d 3.