A working head for an apparatus for mounting and demounting a tyre to and from a corresponding rim (C) of a vehicle wheel, the working head comprising: - a contoured element , having a first end and a second end , spaced from each other along a longitudinal orientation (L), wherein the first end faces in a first direction (V1) and defines a connecting zone of the contoured element and the second end faces in a second direction (V2), opposite to the first direction (V1) and defines a supporting zone of the contoured element , adapted to abut against the wheel rim with the contoured element in sliding contact with the rim (C), the contoured element including a demounting guide , adapted to come into sliding contact to guide the wheel tyre, and a mounting guide , juxtaposed with the demounting guide along a transverse orientation (T) perpendicular to the longitudinal orientation (L) and adapted to come into sliding contact to guide the tyre while it is being mounted to the wheel rim (C); - a gripping tool , movable in a working plane perpendicular to the transverse orientation (T) and parallel to the longitudinal direction between a gripping position (PP), where it is operatively interposed between the rim and the tyre, and a prising position (PS), where the gripping tool is lifted longitudinally relative to the second end of the contoured element ; a transmission unit connectable to an actuator and to the gripping tool and configured to move the gripping tool between the gripping position (PP) and the prising position (PS) responsive to a movement of the actuator , wherein the demounting guide is interposed, along the transverse orientation (T), between the gripping tool and the mounting guide of the contoured element , and wherein the contoured element is removably connected to an arm of the apparatus , characterized in that the contoured element is made as a single part, made of polymeric material. - a contoured element , having a first end and a second end , spaced from each other along a longitudinal orientation (L), wherein the first end faces in a first direction (V1) and defines a connecting zone of the contoured element and the second end faces in a second direction (V2), opposite to the first direction (V1) and defines a supporting zone of the contoured element , adapted to abut against the wheel rim with the contoured element in sliding contact with the rim (C), the contoured element including a demounting guide , adapted to come into sliding contact to guide the wheel tyre, and a mounting guide , juxtaposed with the demounting guide along a transverse orientation (T) perpendicular to the longitudinal orientation (L) and adapted to come into sliding contact to guide the tyre while it is being mounted to the wheel rim (C); - a gripping tool , movable in a working plane perpendicular to the transverse orientation (T) and parallel to the longitudinal direction between a gripping position (PP), where it is operatively interposed between the rim and the tyre, and a prising position (PS), where the gripping tool is lifted longitudinally relative to the second end of the contoured element ; a transmission unit connectable to an actuator and to the gripping tool and configured to move the gripping tool between the gripping position (PP) and the prising position (PS) responsive to a movement of the actuator , wherein the demounting guide is interposed, along the transverse orientation (T), between the gripping tool and the mounting guide of the contoured element , and wherein the contoured element is removably connected to an arm of the apparatus , characterized in that the contoured element is made as a single part, made of polymeric material. <EOS>