In antiferromagnetic crystals the results of AFMR, when combined with other data, yield the anisotropy K. By subtracting the magnetic dipolar anisotropy KMD from K, the fine structure anisotropy KFS is found. For Cr2O3, the KMD computation of Tachiki and Nagamiya, 0.059 cm−1/ion, had been accepted as a basis for further analyses. However, in the course of computing KMD by modern machine methods for various sesquioxide antiferromagnets, we have found this value to be inappropriate. The Shull magnetic structure (c) to which Cr2O3 belongs is one in which the magnetic geometry effectively is almost cubic! The computed KMD value thus is sensitive to small changes in lattice geometry. Presently accepted room-temperature crystal parameters yield KMD = 0.0088 cm−1/ion, ⅙ the former result; consequently Cr2O3 AFMR data have been reanalyzed. The temperature behavior of KFS and KMD in pure Cr2O3 and in (Cr1−fAlf)2O3 crystals is discussed. Similar KMD calculations have been made for the Ti, V, and Fe sesquioxides. In the case of α-Fe2O3 we have been able to predict, with the use of AFMR data, the spin-flip near 263°K. The experimentally found decrease of this spin-flip temperature with increasing f in the α(Fe1−fAlf)2O3 system is discussed in the light of existing information.