A connecting device arranged between a steering wheel and a pitman module of a motor vehicle encompasses a stator part and a rotor part accommodated therein for enclosing a flexible line comprising several individual electrical conductors, is taken up with its two wide sides via a U-shaped turning section with several windings onto the axially aligned inner wall of the rotor part and spaced apart, and conversely said line is taken up with several additional windings onto the likewise axially aligned outer wall of the stator part, and is held with its two narrow sides between the radially aligned base which in the area of the inner wall is a component of the rotor part and in the area of the outer wall is a component of the stator part, and the radially aligned cover wall of the rotor part. The base and/or the cover wall are designed so that between the inner wall and the outer wall said walls only form sections of a supporting surface for the narrow sides of the line.