Method of honing bores

In a method for honing a bore having first and second sections sequentially arranged in an axial direction of the bore, wherein the first section is hardened so that the first and second sections have different hardness, a honing tool is radially supported by positioning guides of the honing tool on the second bore section. first section is machined with honing stones arranged on the honing tool to remove material from the first section. During machining of the first section, the honing tool is expanded by feeding the honing stones according to a defined feeding mode against a surface of the first section by a force-guided electro-mechanical advancement. During machining of the first section, the working stroke of the honing tool is adjusted continuously at least toward the end of the honing process. Feeding of the guides is realized independently of feeding of the honing stones.