Magnetically induced dielectric anisotropy (MDA) has been studied in concentrated suspensions of magnetite in paraffin (n-hexadecane). The volumetric fraction was phi =0.3. The maximum value for the applied magnetic field was 48 kA m-1. A clear trend to the saturation in MDA was found for applied fields larger than 32 kA m-1. In this case, the dielectric anisotropy is up to 15% of the dielectric constant at zero field. A constant value for g=1.23 was found for magnetic fields higher than 12 kA m-1 (g=( epsilon /sub ///- epsilon (0))/( epsilon (0)- epsilon perpendicular to ) where epsilon (0) is the dielectric constant at null field). Below this field, a transition to g=1 was attained at 4 kA m-1. These results disagree with the value g=2 theoretically deduced for ideally monodispersive suspensions in the overall field range. The present results are tentatively explained qualitatively and quantitatively taking into account the mechanism of particle aggregation.