Anisotropy of low-field magnetic susceptibility (AMS) of basaltic lava flows can give some clues about post-emplacement tilting occurring in volcanic sequences. Such a study has been carried out on a sequence of 19 successive lava flows from Kerguelen Archipelago. Surprisingly, two different patterns were observed. The first one - herein called normal fabric - is consistent with the lava-flow direction inferred from geological observations, whereas the second one observed for about 70 per cent of the analysed samples - herein called abnormal fabric - appears to be unrelated to the shear history of the lava flows during their emplacements. These abnormal fabrics are not strictly inverse fabric but seem to have a more complex origin. The unusual nature of these abnormal fabrics has been confirmed by lattice preferred orientation of plagioclases obtained from high-resolution electron backscattered diffraction measurements. The aim of this study is to propose a physical interpretation of these fabrics. A first step in our understanding was to clearly identify the nature and the magnetic properties of the Fe-Ti oxides assemblage. Thus, we present a comprehensive rock magnetic analysis relying on low- and high-temperature thermomagnetic curves (K-T), crossover diagrams, first-order reversal curves, ore-microscopy, Mössbauer measurements and electron backscattered images. We found that in the present case the abnormal fabrics are probably linked to a mixture of prevailing single domain (SD) strongly interacting grains population and a subsidiary multidomain grains population. SD grains are identified as small magnetite crystallized within the interstitial glass in globular aggregates along the silicate framework. Then a question arises: to what extent such SD interacting grains in globular aggregates can affect the magnetic susceptibility and its anisotropy? To answer this question, we developed a physical model in which the total energy density of an SD grain with an uniaxial anisotropy is minimized. In this model, the distribution function of the direction of the magnetic interaction field is comprised between two boundary states. It is either isotropic, which formally corresponds to the thermal demagnetized state, or it is ordered, which formally corresponds to the Alternative Field demagnetized state. We show that in both cases the degree of anisotropy decreases as the interaction field increases. Thus, we conclude that the abnormal fabric encountered in this study can be simply explained by strong magnetostatic interactions that would explain the large scattering of AMS often observed in basaltic lava flows.