Abstract: A method and apparatus for machining of bores in workpieces is described, where a honing tool, covered with an abrasive material coating and radially pressed against the wall of the bore, simultaneously performs a rotational motion and an axial reciprocal motion. In addition to the reciprocal and rotational motions, the honing tool performs a high-frequency, short-stroke self-oscillation, which is excited by ultrasonic oscillation in the range of 16 to 40 kHz.