Hand-held and hand-guided random orbital polishing or sanding power tool, comprising a static body, a motor, an eccentric element driven by the motor and performing a rotational movement about a first rotational axis, and a plate-like backing pad connected to the eccentric element in a manner freely rotatable about a second rotational axis, wherein the first and second rotational axes (10, 16) extend essentially parallel to one another and are spaced apart from one another, wherein at least part of an external circumferential surface of the eccentric element has an at least discrete rotational symmetry in respect to the first rotational axis; and wherein the power tool comprises at least one first bearing provided between the rotationally symmetric part of the external circumferential surface of the eccentric element and the static body of the power tool so that the eccentric element is guided in respect to the body in a manner rotatable about the first rotational axis; and wherein the power tool comprises a mechanical gear arrangement with at least two meshing gear wheels (27, 28, 29, 29.1, 29.2), wherein the gear arrangement is provided functionally between a driving shaft driven by the motor and the eccentric element and wherein at least one of the gear wheels is attached to the eccentric element in a manner adapted for transmitting torque to the eccentric element characterized in that the mechanical gear arrangement is designed as a planetary gear arrangement comprising a sun gear wheel, a ring gear wheel and a plurality of planetary gear wheels meshing the sun gear wheel and the ring gear wheel, wherein the planetary gear wheels are attached to the eccentric element in a freely rotatable manner, wherein the ring gear wheel is attached to the static body of the power tool in a torque proof manner or forms an integral part therewith; or the mechanical gear arrangement comprises a first central gear wheel, a plurality of first pinion gear wheels (29.1) meshing the first central gear wheel, a plurality of second pinion gear wheels (29.2) each located coaxial to one of the first pinion gear wheels (29.1) and attached thereto in a torque proof manner or forming an integral part of the respective first pinion gear wheel (29.1), and a second central gear wheel meshing the second pinion gear wheels (29.2), wherein the second central gear wheel is attached to the eccentric element in a torque proof manner or the second central gear wheel forms an integral part of the eccentric element. at least part of an external circumferential surface of the eccentric element has an at least discrete rotational symmetry in respect to the first rotational axis; and wherein the power tool comprises at least one first bearing provided between the rotationally symmetric part of the external circumferential surface of the eccentric element and the static body of the power tool so that the eccentric element is guided in respect to the body in a manner rotatable about the first rotational axis; and wherein the power tool comprises a mechanical gear arrangement with at least two meshing gear wheels (27, 28, 29, 29.1, 29.2), wherein the gear arrangement is provided functionally between a driving shaft driven by the motor and the eccentric element and wherein at least one of the gear wheels is attached to the eccentric element in a manner adapted for transmitting torque to the eccentric element characterized in that the mechanical gear arrangement is designed as a planetary gear arrangement comprising a sun gear wheel, a ring gear wheel and a plurality of planetary gear wheels meshing the sun gear wheel and the ring gear wheel, wherein the planetary gear wheels are attached to the eccentric element in a freely rotatable manner, wherein the ring gear wheel is attached to the static body of the power tool in a torque proof manner or forms an integral part therewith; or the mechanical gear arrangement comprises a first central gear wheel, a plurality of first pinion gear wheels (29.1) meshing the first central gear wheel, a plurality of second pinion gear wheels (29.2) each located coaxial to one of the first pinion gear wheels (29.1) and attached thereto in a torque proof manner or forming an integral part of the respective first pinion gear wheel (29.1), and a second central gear wheel meshing the second pinion gear wheels (29.2), wherein the second central gear wheel is attached to the eccentric element in a torque proof manner or the second central gear wheel forms an integral part of the eccentric element.