A process of effecting necrosis of neoplasms in warm blooded animals as a result of hyperthermia of the neoplasm includes injecting particles into the warm blooded animals in proximity of the neoplasm. The particles are capable of exhibiting hysteresis heating when subjected to an alternating magnetic field. Further, the particles are of a size of at least two microns, or greater, so as to be incapable of being intracellularly absorbed within the cells of either the viable tissue of the animal or the neoplastic tissue. After interjecting the particles in association with the neoplasm, the area of the neoplasm is then subjected to an alternating magnetic field. This field is of a frequency greater than that sufficient to cause any appreciable neuromuscular response to the alternating magnetic field, and is less than that capable of causing any detrimental eddy current heating and/or dielectric heating of viable healthy tissue of the warm blooded animal. The neoplasm is maintained within the field for a time sufficient to heat the particles and the neoplasm, with which the particles are associated, to a temperature of at least 42.degree. C. to cause necrosing of the neoplasm.