We present and interpret anisotropy of magnetic susceptibility (AMS) fabrics in various rocks, focusing on the effects of Alternating Field (AF) demagnetization and Isothermal Remanent Magnetization (IRM). Our findings reveal that AMS in samples from intrusive rocks with large multidomain magnetite grains is minimally affected by IRM or static AF demagnetization. In nearly isotropic volcanic rocks with titanomagnetite pseudo single domain (PSD) carriers, AMS fabrics caused by static AF demagnetization are easily identifiable, with the most prominent effect being a well-defined AMS lineation (up to 1.04) in the direction of the applied AF demagnetization. Conversely, in samples from rapidly cooled volcanic rocks with titanomagnetite of smaller magnetic grain size, an AMS foliation (similar to 1.02) is observed orthogonal to the direction of the applied AF field, instead of a lineation. In such samples, an IRM produces a much larger AMS foliation up to 1.3 orthogonal to the IRM. The IRM-impressed AMS is also particularly strong in metamorphic rocks in the greenschist facies with either titano-hematite or pyrrhotite magnetic carriers. Samples with the largest IRM-impressed fabric have very high M-rs/M-s ratio (>similar to 0.4). M-rs/M-s ratios above 0.5 may indicate the contribution of SD magnetic grains with multiaxial anisotropy. As the apparent multiaxial anisotropy is especially observed in volcanic rocks with micron size dendrites of titanomagnetites, the complex shape of the magnetic particles and their chemical composition likely play a key role in IRM-impressed AMS. AMS fabric in volcanic rocks should not be measured after static AF demagnetization. Tumbling AF demagnetization does not alter significantly the initial magnetic fabric and could be safely used in rocks with strong magnetization related to lightning possibly recording an IRM impressed AMS.