Tool-holder unit of a machine for machining block or slab materials, said tool-holder unit being moveable above a working plane of said machine on which the block or slab material to be machined is laid, wherein the tool-holder unit comprises: - a spindle on which a circular blade can be mounted, and - a coupling assembly for removably coupling a second machining tool (28, 128) to a front free end of the spindle, comprising: a) a tool-holder associated to the second machining tool (28, 128); b) at least one mechanical coupling device provided with elements cooperating in abutment relationship (58, 68) to make the tool-holder and the spindle rotationally integral with each other; and c) a first axial locking element of the tool-holder configured to removably lock in translation and in a substantially axial direction said tool-holder on the spindle, said first axial locking element comprising a magnetic fixing device of the tool-holder to the spindle; characterised in that said coupling assembly further comprises: d) a substantially cylindrical shank extending from said free end of the tool-holder; e) a substantially cylindrical housing seat of said shank, axially positioned in said spindle or, if present, in a tool-holder coupling element associated to the front free end of the spindle; and f) at least a second axial locking element of the tool-holder, configured to removably lock in translation and in a substantially axial direction said tool-holder in the spindle, said at least a second axial locking element being translationally movable in radial direction to removably lock said shank in the respective housing seat. - a spindle on which a circular blade can be mounted, and - a coupling assembly for removably coupling a second machining tool (28, 128) to a front free end of the spindle, comprising: a) a tool-holder associated to the second machining tool (28, 128); b) at least one mechanical coupling device provided with elements cooperating in abutment relationship (58, 68) to make the tool-holder and the spindle rotationally integral with each other; and c) a first axial locking element of the tool-holder configured to removably lock in translation and in a substantially axial direction said tool-holder on the spindle, said first axial locking element comprising a magnetic fixing device of the tool-holder to the spindle; characterised in that said coupling assembly further comprises: d) a substantially cylindrical shank extending from said free end of the tool-holder; e) a substantially cylindrical housing seat of said shank, axially positioned in said spindle or, if present, in a tool-holder coupling element associated to the front free end of the spindle; and f) at least a second axial locking element of the tool-holder, configured to removably lock in translation and in a substantially axial direction said tool-holder in the spindle, said at least a second axial locking element being translationally movable in radial direction to removably lock said shank in the respective housing seat. a) a tool-holder associated to the second machining tool (28, 128); b) at least one mechanical coupling device provided with elements cooperating in abutment relationship (58, 68) to make the tool-holder and the spindle rotationally integral with each other; and c) a first axial locking element of the tool-holder configured to removably lock in translation and in a substantially axial direction said tool-holder on the spindle, said first axial locking element comprising a magnetic fixing device of the tool-holder to the spindle; d) a substantially cylindrical shank extending from said free end of the tool-holder; e) a substantially cylindrical housing seat of said shank, axially positioned in said spindle or, if present, in a tool-holder coupling element associated to the front free end of the spindle; and f) at least a second axial locking element of the tool-holder, configured to removably lock in translation and in a substantially axial direction said tool-holder in the spindle, said at least a second axial locking element being translationally movable in radial direction to removably lock said shank in the respective housing seat.