A connecting device (10) having a connector device (1) for integrating a double hose line (9) comprises a connector (2) that can be inserted into the end of the hose line (9) and has a plug-in body (22) and a connecting base (21) and a line connecting part (6) that can be connected thereto. In the region of the hose integration, flow disruptions and capture areas are to be prevented at the flow transition point (12) between the connector (2) and line connecting part (6). A circumferential bead-shaped connecting edge (920) of an inner hose (92) located outside the flow cross-section engages in a recessed connecting groove (7) between the connector (2) and the line connecting part (6), wherein the connecting edge (920) has the same shape as the connecting groove (7) in terms of the cross-section. The connecting groove (7) connects to an inner opening edge (4) at the connecting base (21) on the transition point (12) between the connector (2) and the line connecting part (6) and is aligned at an acute angle (A) to the flow and line direction (S). An opening slit (71) having a slit width that corresponds to the wall thickness of the inner hose (92) is configured at the transition point (12) between the opening edge (4) and a peripheral edge (62). The connecting groove (7) is widened compared to the opening slit (71). The peripheral edge (62) of the line connecting part (6) forms a clamping contact for the bead-shaped delivery hose connecting edge (92) at the transition point (12) at a flat angle (F) to the straight line/flow direction (S).