A system for determining the state of shear deformation of a crown portion of a tyre (1) during the running of a motor vehicle (7) comprises at least one sensor (11; 111; 211) and processing means (15) operatively associated with said sensor; the system further comprises at least one magnetic field generator (10; 110; 210) applied to the tyre (1); said sensor (11; 111; 211) is capable of detecting magnetic induction and is associated with said generator (10; 110; 210) to supply a signal indicating the electrical potential difference which is generated within said sensor in the presence of the magnetic field; this signal represents the variation with time of the shear deformation of the crown portion of the tyre (1).