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Magnetisation reversal processes of microstructured NiFe rings are studied by fringing-field-induced local Hall effect (LHE) and numerical model calculations. This semiconductor-based technique yields a high sensitivity of magnetic stray fields and allows the authors to detect magnetisation hysteresis loops of single NiFe rings. For narrow rings, sharp transitions from so called 'onion' to the 'vortex' state are detected. Only onion and global vortex states are possible magnetisation configurations in narrow rings. In rings with smaller inner diameter, the transitions are more complex. The minor loop analysis of rings shows that onion and global vortex states are stable and independent of the magnetic history, but the local vortex state depends on the way the magnetic field has been swept beforehand. The switching fields can be controlled by the inner diameter in good agreement with the computational results.