Connection system for pipes, comprising a core and a nut, wherein the core comprises an at least partially cylindrical bore that extends axially symmetrically along a longitudinal axis, wherein the nut comprises a front rim with a bore adapted to insert a pipe and a rear rim with a bore adapted to insert the core, wherein a sealing and a gripping element are arranged in an inner space defined by the core and the nut, wherein in a first state of the connection system - the core and the nut are moveable relative to each other parallel to the longitudinal axis, and - the gripping element in its relaxed state defines an inner bore with a maximum mean insertion diameter (D 6max); wherein in a second state (B, B 1, B 2, B 3) of the connection system - first holding means formed at the core are in engagement with second holding means formed at the nut, to secure the core and the nut against displacement relative to each other, - the gripping element is supported by a compression surface of the nut holding the gripping element in a compressed state in which the inner bore of the gripping element is reduced to a mean gripping diameter (D 6G), - wherein the nut is adapted to exert a force acting parallel to the longitudinal axis that presses the gripping element against at least one of the sealing, an intermediate element, and a gripping shoulder formed at the inner side of the core wherein the nut comprises at least one nut locking protrusion extending parallel to the longitudinal axis and radially inwardly from the rear rim of the nut and the core comprises at least one core locking protrusion extending radially outwardly from the core, wherein in the first state and/or in the second state (B, B 1, B 2, B 3) of the connection system the core locking protrusion and the nut locking protrusion engage with each other to prevent rotational movements of the nut relative to the core in one rotational direction. comprising a core and a nut, wherein the core comprises an at least partially cylindrical bore that extends axially symmetrically along a longitudinal axis, wherein the nut comprises a front rim with a bore adapted to insert a pipe and a rear rim with a bore adapted to insert the core, wherein a sealing and a gripping element are arranged in an inner space defined by the core and the nut, wherein in a first state of the connection system - the core and the nut are moveable relative to each other parallel to the longitudinal axis, and - the gripping element in its relaxed state defines an inner bore with a maximum mean insertion diameter (D 6max); - the core and the nut are moveable relative to each other parallel to the longitudinal axis, and - the gripping element in its relaxed state defines an inner bore with a maximum mean insertion diameter (D 6max); wherein in a second state (B, B 1, B 2, B 3) of the connection system - first holding means formed at the core are in engagement with second holding means formed at the nut, to secure the core and the nut against displacement relative to each other, - the gripping element is supported by a compression surface of the nut holding the gripping element in a compressed state in which the inner bore of the gripping element is reduced to a mean gripping diameter (D 6G), - wherein the nut is adapted to exert a force acting parallel to the longitudinal axis that presses the gripping element against at least one of the sealing, an intermediate element, and a gripping shoulder formed at the inner side of the core - first holding means formed at the core are in engagement with second holding means formed at the nut, to secure the core and the nut against displacement relative to each other, - the gripping element is supported by a compression surface of the nut holding the gripping element in a compressed state in which the inner bore of the gripping element is reduced to a mean gripping diameter (D 6G), - wherein the nut is adapted to exert a force acting parallel to the longitudinal axis that presses the gripping element against at least one of the sealing, an intermediate element, and a gripping shoulder formed at the inner side of the core wherein the nut comprises at least one nut locking protrusion extending parallel to the longitudinal axis and radially inwardly from the rear rim of the nut and the core comprises at least one core locking protrusion extending radially outwardly from the core, wherein in the first state and/or in the second state (B, B 1, B 2, B 3) of the connection system the core locking protrusion and the nut locking protrusion engage with each other to prevent rotational movements of the nut relative to the core in one rotational direction.