Honing tool (100, 400) for machining an inner face of a bore in a workpiece with the aid of at least one honing operation, in particular for honing cylinder surfaces in the production of cylinder blocks or cylinder liners for reciprocating piston engines, comprising: a tool body that defines a tool axis (112, 412); an expandable cutting group (130, 430), attached to the tool body, having a plurality of radially feedable cutting material body carriers (150-1, 150-2, 450-1, 450-2) that each cover a circumferential angle range and are feedable radially with respect to the tool axis (112, 412) by means of a cutting group feeding system assigned to the cutting group (130, 430), wherein each cutting material body carrier (150-1, 150-2, 450-1, 450-2) carries, on its radial outer side (154, 454), a plurality of narrow cutting material bodies (140-1, 140-2, 140-3) configured as cutting material strips (140-1, 140-2, 140-3, 440-1, 440-2) that are narrow in the circumferential direction and have a width in the circumferential direction that is small compared with the axial length of the cutting material strips, wherein the cutting material bodies (140-1, 140-2, 140-3) are arranged at a mutual spacing from one another, characterized in that the honing tool (100, 400) is designed as a honing tool with double expansion, wherein the cutting group (130, 430) has a first group of cutting material body carriers (450-1, 450-2, 450-5, 450-6) and a second group of cutting material body carriers (450-3, 450-4, 450-7, 450-8) that is feedable independently of the first group, in the first group, the cutting material bodies are fastened directly to the associated cutting material body carrier without interposition of an elastic intermediate layer and are connected rigidly to the cutting material body carrier and, in the second group, the cutting material bodies are fastened to the associated cutting material body carrier in an individually resilient manner via an elastic intermediate layer (160, 560, 660, 760, 860, 960), wherein the elastic intermediate layer (160, 560, 660, 760, 860, 960) is arranged in an intermediate space between a cutting material body and the cutting material body carrier (150-1, 150-2, 450-1, 450-2) carrying the cutting material body, and fills the intermediate space between the cutting material body and the cutting material body carrier. a tool body that defines a tool axis (112, 412); an expandable cutting group (130, 430), attached to the tool body, having a plurality of radially feedable cutting material body carriers (150-1, 150-2, 450-1, 450-2) that each cover a circumferential angle range and are feedable radially with respect to the tool axis (112, 412) by means of a cutting group feeding system assigned to the cutting group (130, 430), wherein each cutting material body carrier (150-1, 150-2, 450-1, 450-2) carries, on its radial outer side (154, 454), a plurality of narrow cutting material bodies (140-1, 140-2, 140-3) configured as cutting material strips (140-1, 140-2, 140-3, 440-1, 440-2) that are narrow in the circumferential direction and have a width in the circumferential direction that is small compared with the axial length of the cutting material strips, wherein the cutting material bodies (140-1, 140-2, 140-3) are arranged at a mutual spacing from one another, characterized in that the honing tool (100, 400) is designed as a honing tool with double expansion, wherein the cutting group (130, 430) has a first group of cutting material body carriers (450-1, 450-2, 450-5, 450-6) and a second group of cutting material body carriers (450-3, 450-4, 450-7, 450-8) that is feedable independently of the first group, in the first group, the cutting material bodies are fastened directly to the associated cutting material body carrier without interposition of an elastic intermediate layer and are connected rigidly to the cutting material body carrier and, in the second group, the cutting material bodies are fastened to the associated cutting material body carrier in an individually resilient manner via an elastic intermediate layer (160, 560, 660, 760, 860, 960), wherein the elastic intermediate layer (160, 560, 660, 760, 860, 960) is arranged in an intermediate space between a cutting material body and the cutting material body carrier (150-1, 150-2, 450-1, 450-2) carrying the cutting material body, and fills the intermediate space between the cutting material body and the cutting material body carrier.