A machine for fitting and removing wheel tires for vehicles includes a supporting structure of a clamping and rotating device for clamping and rotating the wheel rim and an operating head for fitting/removing a tire onto/from the rim. The operating head has a removal tool associated with a first actuator and turnable between a first clamping position in which the tool is tilted towards the rotation axis of the rim, and a second entrainment position in which the tool extends along a direction substantially parallel to the rotation axis of the rim. The operating unit includes an arrangement for transforming the movement generated by a second actuator into the sideways movement of the operating head along a curved direction and near and away to a section of the annular flange of the rim.