Synthetic and very pure single crystals of nickel iodine boracite (Ni3B7O13I, NIB), up to 10 mm in their largest dimension grown by a chemical transport process were investigated, using a self-compensating recording balance under quasistatic conditions. Below 64°K ferromagnetic behavior in agreement with the results of Ascher, Rieder, Schmid, and Stössel was observed. Rotation diagrams showed a slight hexagonal component in the (111) plane of the crystal. In the (100) plane, however, large tetragonal torsion moments were recorded having frequent discontinuities and very large rotational hysteresis in fields of about 5 kOe. In a temporally and spatially constant magnetic field, a discontinuous but on the average linear decrease of the torsion moment was observed, taking about 30 min for it to vanish completely. The above behavior can be only partly explained on the basis of ferromagnetic-domain wall motion. The influence of ferroelectric-domain processes coupled through ferromagnetoelectric interaction seems to be of considerable importance for the relaxation of magnetization and is therefore assessed and discussed.