A brake caliper of a disc brake has a caliper body straddling a brake disc and having a thrust device housing accommodating a thrust device operatively connected to a translating screw nut. The translating screw nut is operatively connected to a worm. The worm is operatively connected to a gearbox and rotatably supported by a screw thrust bearing configured to apply for the worm an axial reaction. At least one part of the gearbox is rotatably supported by a gearbox thrust bearing configured to apply for the at least one part of the gearbox a radial reaction. The thrust bearing has at least one radially inner slewing ring and the gearbox has an epicyclic gear having a fixed gear or an internally toothed body cooperating with at least one planet gear rotatably supported about at least one planet gear pin connected to the at least one radially inner slewing ring to transmit action of the gearbox to the worm by the at least one radially inner slewing ring.