A method for producing a multi-core cable includes arranging first and second contact elements in a contact carrier having first and second longitudinal channels connecting a contacting side to a cable side, and first and second through-openings respectively crossing the first and second longitudinal channels, and a second through-opening crossing the second longitudinal channel. The first and second longitudinal channels and the first and second through-openings are sealed in a fluid-tight manner by inserting two first sealing pieces into the first through-opening and two second sealing pieces into the second through-opening. In an injection-molding method, a connecting piece is formed connecting the contact carrier to the outer sheath of the cable by overmolding at least a rear section of the contact carrier comprising the first and second through-openings and a section of the cable protruding on the cable side.