"The subject of the project is the magnetodynamics of single-domain ferromagnetic nanoparticles driven by strong ac magnetic fields. The phenomenon of prime interest here is dynamic magnetic hysteresis (DMH) . The main important applications of DMH are (i) magnetic moment switching (under pulsed fields) in magnetic data storage and (ii) heat generation in magnetically induced hyperthermia (medical as well as other applications). Nowdays local magnetic hyperthermia is one of the most promising approaches in addition to chemical and radiological methods for cancer treatment. Unfortunately, the progress is hampered by the lack of reliable understanding of the laws governing the interplay between internal (magnetic relaxation) and external (viscous dissipation due to mechanical rotation) losses and their joint effect on heat generation. There also exists a ""no-man land"" between two limiting frameworks: (i) natural (intrinsic) magnetic resonance where the magnetic moment precession is due to the internal field and (ii) the standard (Zeeman) magnetic resonance where the main factor in the precession is dominated by a strong external field while the internal field is merely a perturbation. In the second case, substantial increase in the absorption can be achieved which is important for hyperthermia. We are going to study magnetodynamics and energy absorption in solid and liquid suspensions of magnetic nanoparticles by developing analytical and numerical techniques for treating effects of dissipation to the surrounding heat bath in DMH. The results obtained from analytical and numerical solutions of the Gilbert-Landau-LIfshitz equation augmented by a random field term will be compared with available experimental observations."