In order to drift underground roads, tunnelling machines are used that have a rotatively driven boring head base body, a rigid first bit and rail heads that can radially sweep around axes of rotation between the working point in the conductor shaft and the gallery faces by means of thrusting piston gears and that carry at least one roller boring tool. In order to improve the coordination between the opening of the conductor shaft and undercutting, that are carried out simultaneously, the first bit (2) is designed as a ring borer (2) that breaks out a drilling core (3) through slits of an annular cavity (4). The ring borer (2) has two parallel arms (6) spaced apart from a central axis (5) that carry boring tools (7) articulated on a cross-beam (10) of a carrying frame (9) that has an advancing device (11). The carrying frame (9) surrounds the thrusting piston gears (18) for the radially sweeping rail heads (12), is perpendicularly arranged to the rail heads (12) and extends parallel to the central axis (5) at the boring head base body (1).