Tyre-changing machine for fitting and removing vehicle wheels, comprising: - at least a bed for resting on the ground; - at least a spindle which extends from said bed and on which is mountable at least a wheel having a rim and a tyre with two opposite flanks (F1, F2), said spindle being configured to tighten said rim on it and able to put in rotation said wheel around an axis of rotation; and - two bead breaking tools (32, 42) which are movable one towards the other in the proximity of said spindle along a bead-breaking direction substantially parallel to said axis of rotation of the spindle, said bead breaking tools (32, 42) having respective non-rolling contact surfaces (34, 44) able to contact and push in use said opposite flanks (F1, F2) with said wheel mounted on said spindle; characterized by the fact that said non-rolling contact surfaces (34, 44) are substantially curved with the concavity thereof facing said axis of rotation, and the position and/or movement of said bead breaking tools (32, 42) can be stored in an electronic memory for: - pressing said bead breaking tools (32, 42) on a surface of said opposite flanks (F1, F2) corresponding to a circular sector of the circumference of said wheel to remove said tyre in correspondence to said circular sector; - moving said bead breaking tools (32, 42) away from said opposite flanks (F1, F2); - rotating said spindle and said wheel around said axis of rotation to shift said circular sector with respect to said bead breaking tools (32, 42) moved away; - repeating said pressing, said moving away and said rotating on different circular sectors to remove the complete tyre t, wherein in said repeating the different circular sectors are adjacent and together cover the entire circumference of said opposite flanks (F1, F2). - at least a bed for resting on the ground; - at least a spindle which extends from said bed and on which is mountable at least a wheel having a rim and a tyre with two opposite flanks (F1, F2), said spindle being configured to tighten said rim on it and able to put in rotation said wheel around an axis of rotation; and - two bead breaking tools (32, 42) which are movable one towards the other in the proximity of said spindle along a bead-breaking direction substantially parallel to said axis of rotation of the spindle, said bead breaking tools (32, 42) having respective non-rolling contact surfaces (34, 44) able to contact and push in use said opposite flanks (F1, F2) with said wheel mounted on said spindle; - pressing said bead breaking tools (32, 42) on a surface of said opposite flanks (F1, F2) corresponding to a circular sector of the circumference of said wheel to remove said tyre in correspondence to said circular sector; - moving said bead breaking tools (32, 42) away from said opposite flanks (F1, F2); - rotating said spindle and said wheel around said axis of rotation to shift said circular sector with respect to said bead breaking tools (32, 42) moved away; - repeating said pressing, said moving away and said rotating on different circular sectors to remove the complete tyre t, wherein in said repeating the different circular sectors are adjacent and together cover the entire circumference of said opposite flanks (F1, F2).