We observed a few magnetic relaxation phenomena in a LuFeMgO4single crystal, that is, the difference in the magnetization between field-cooled and zero-field-cooled specimens, the appearance of thermoremanent magnetization, and the frequency dependence of the cusp temperature of AC susceptibility. The observed relaxation was interpreted in terms of thermal fluctuations and freezing of the magnetic clusters which are supposed to exist in this substance. © 1995, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.