A connection device comprising - a line section (10, 10", 10"', 10"") having, at its end, a radially outwardly protruding abutment flange (14, 14", 14"', 14"") for butting against a corresponding abutment flange of a further line section to be coupled to said line section (10, 10", 10"', 10""), and - an annular connection clamp having a radially inwardly protruding first clamping flange (22, 22", 22"', 22"") and an axial abutment (24, 24", 24"', 241"") spaced apart axially from said first clamping flange, and being made up of a first and a second half-ring segment (20, 20", 20"', 20""), each of which having a first and a second segment end, wherein the first segment end of the first half-ring segment (20, 20", 20'", 20"") has latching means (281, 281", 281"', 281"") of a first type and the second segment end of the second half-ring segment has corresponding latching means (282, 282", 282"', 282"") of a second type, which are pushed into one another in a tangential direction, thereby being latchable together, wherein the second segment end of the first half-ring segment (20, 20", 20'", 20"") has latching means (282, 282", 282"', 282"") of the second type and the first segment end of the second half-ring segment has latching means (281, 281", 281"', 281'"") of the first type, which are pushed into one another in a tangential direction, thereby being latchable together, wherein the line section is designed in the form of a tubular connection stub (10, 10", 10"', 10"") having first thread means (16, 16", 16'", 161"") spaced apart axially from the abutment surface (141, 141", 141'", 141"") of its abutment flange (14, 14", 14"', 14""), and the axial abutment (24, 24", 24"', 241"") of the connection clamp is embodied as second thread means (24, 24", 24'", 241"") corresponding to the first thread means (16, 16", 16"', 161""), characterized in that either the connection stub (10, 10", 10'") has a tangentially extending first linear guide element (181, 181", 181"') and one of the half-ring segments (20, 20", 20"') has a corresponding second linear guide element (261, 261", 261"') on the interior wall of one of its segment ends, or the connection stub (10"") has a radially extending first linear guide element (181"") and one of the half-ring segments (20"") has, as a part of the wall of one of its segment ends, a corresponding second linear guide element (261""), wherein in both cases during an interaction of the first and second linear guide element both an axial movement and a rotation of the half-ring segment relative to the connection stub are restricted. - a line section (10, 10", 10"', 10"") having, at its end, a radially outwardly protruding abutment flange (14, 14", 14"', 14"") for butting against a corresponding abutment flange of a further line section to be coupled to said line section (10, 10", 10"', 10""), and - an annular connection clamp having a radially inwardly protruding first clamping flange (22, 22", 22"', 22"") and an axial abutment (24, 24", 24"', 241"") spaced apart axially from said first clamping flange, and being made up of a first and a second half-ring segment (20, 20", 20"', 20""), each of which having a first and a second segment end, wherein the first segment end of the first half-ring segment (20, 20", 20'", 20"") has latching means (281, 281", 281"', 281"") of a first type and the second segment end of the second half-ring segment has corresponding latching means (282, 282", 282"', 282"") of a second type, which are pushed into one another in a tangential direction, thereby being latchable together, wherein the second segment end of the first half-ring segment (20, 20", 20'", 20"") has latching means (282, 282", 282"', 282"") of the second type and the first segment end of the second half-ring segment has latching means (281, 281", 281"', 281'"") of the first type, which are pushed into one another in a tangential direction, thereby being latchable together,