Rotational hysteresis losses Wr were determined as a function of magnetic field H for dispersed spherical Fe3O4 particles of mean grain sizes 85 nm, 127 nm and 162 nm between 78 K and 294 K. The observe Wr-H curves are compared with theoretical curves for single domain particles. The analysed particles reveal centers of high magnetic anisotropy. Such centers can be of importance during the generation of a thermoremanent magnetization, as they may be the origin of enhanced magnetic stability. ¿ American Geophysical Union 1988