The invention relates to nanoscale particles suited especially for use in tumor therapy by hyperthermia. Said particles comprise a (preferably superparamagnetic) iron oxide-containing core and at least two shells surrounding said core. The (innermost) shell adjoining the core is an envelope which comprises groups capable of forming cationic groups and is broken down by human or animal tissue at such a slow rate as to allow for association of the core surrounded by said envelope with the surface of cells and/or for absorption of said core into the inside of cells. The outer shell(s) consist(s) of species having neutral and/or anionic groups which allow the nanoscale particles to appear to the outside as having a neutral or negative charge and which are broken down by human or animal tissue more rapidly than the innermost shell—and in so doing uncover the shells underneath—but still sufficiently slowly so as to ensure that the nanoscale particles are adequately distributed in a tissue infiltrated with same particles in a particular point.