Abstract: An under-reaming tool for use in preferably horizontal and extended reach bore holes includes a succession of stabilizers, under-reamers and expandable stabilizers. A common drilling mud activator is provided for the expandable elements of under-reamers and expandable stabilizers. A preferred under-reaming device comprises a main body with a number of guiding surfaces distributed over the circumference thereof which have a pitch increasing radially in an axial direction and with a ring collar formed as a piston in a surrounding cylinder housing having a small and a large radial annular surface, and having reaming pads/wings and/or stabilizer pads/wings in sliding contact with a respective guiding surface, the pads being taken up in ports in a jacket surrounding the main body, in such a way that the pads can only be moved radially relative to the jacket, the jacket being attached to or formed as a part of the cylinder housing.