Method and device for producing non-cylindrical bores with at least one recess by honing

A honing tool has a tool body and shells disposed on the tool body. Honing stone sets each provided with two or more honing stones are provided. The shells each support one of the honing stone sets. Guide bars of the honing tool are placed against the bore and a portion of the bore is conically honed with decreasing stroke of the honing tool, wherein a lower reversing point of the honing tool remains substantially unchanged. Honing is terminated as soon as an upper reversing point has reached a predetermined terminal value. Alternatively, a portion of the bore is conically honed with a constant stroke of the honing tool, wherein reversing points of the stroke of the honing tool remain substantially unchanged and a feeding force pressing the honing stones against the bore is controlled as a function of a position of the honing tool in the bore.