Method of honing bores

A method for honing a bore having a first section and a second section sequentially arranged in an axial direction of the bore and possibly not concentric to one another, wherein the first section is hardened so that the first and second sections have different hardness;

• the method comprising the steps of:
• radially supporting a honing tool on a wall of the second section of the bore by feeding guides of the honing tool so as to rest on the wall of the second section of the bore;
• honing the first section with honing stones arranged on the honing tool to remove material from the first section;
• during honing of the first section, expanding the honing tool by feeding the honing stones, independently of feeding the guides, according to a defined feeding mode against a surface of the first section by a force-controlled electro-mechanical advancement;
• during honing of the first section, continuously adjusting a working stroke of the honing tool at least toward the end of the step of honing.