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.

A tool system for configuring honing tools includes at least one tool body that defines a tool axis and an axial bore arranged coaxially to the tool axis, as well as multiple transverse bores oriented perpendicular to the tool axis, wherein the transverse bores form multiple groups around the circumference of the tool body, each group having at least two axially spaced apart transverse bores. The tool system further includes multiple sets of support rail units with guide pins for introducing into transverse bores of a bore group, and also includes at least one set of bolt guide elements for mounting on the tool body, with each set having a bolt guide element for each transverse bore provided for receiving a guide bolt, with a guide bore formed therein, which, when the bolt guide element is mounted on the tool body, runs coaxially with the transverse bore.