The invention relates to a method for producing honed surface structures (5) in workpieces (4) having arbitrary inner and outer contours on widespread, conventional, at least triaxial machining centers. The tools (1) used for this purpose are made of hard-material particles, which can be binded in a pliable matrix made of, for example, elastomers. The honing profile is produced by an effective motion, which is composed of an axially oscillating tool motion and a tool rotation in which the tool circumference rotates slowly or is stationary. The tool (1) is guided along an arbitrary inner or outer contour of the workpiece (4). The application range of honing is expanded by the invention. The workpieces (4) can thus be produced, after machining for example, by a subsequent honing completely in one clamping, which leads to a reduction in the workpiece throughput times and to an increase in the accuracy of the method by avoiding reclamping errors. The investment costs for honing machines and corresponding tools are dispensed with, and even small quantities of high shaping variance can be produced. Inner or outer contours that are not rotationally symmetric can also be honed.