A terminal device has a housing of insulating material, the housing surrounding a portion of the cable end of a sleeve and having a flange directed towards a terminal receptacle. There is additionally provided an inner shield sleeve of conductive material arranged in the housing and surrounding the cable, the inner shield sleeve is connected conductively to a shield of the cable and which has a flanged contact zone directed towards the terminal receptacle. Fastening screws are used simultaneously to press the housing and the flanged contact zone, resting on the housing, of the inner shield sleeve axially against a shield housing of the terminal receptacle.