We report three different experiments performed on permalloy nanorings. They address either (a) the stray-field and (b) the magnetoresistance characteristics of an individual nanoring, or (c) the magnetization dynamics of a periodic array of identical rings. Interestingly, in all three properties covering the frequency range from DC to 20 GHz we observe irreversible switching and hysteretic behavior. Localized spin waves, which are excited by ferromagnetic resonance in different ring segments, are found to obey an intriguing magnetic field dispersion. We attribute this to the characteristic spin configurations in the nanorings, i.e., the onion and the vortex states, which are controlled by the external magnetic field.