A theoretical basis is given for two empirically derived methods of three‐axis alternating field (AF) demagnetization of static samples used initially by Zijderveld and Dunlop to remove “spurious” components of magnetization produced by the AF. It is shown theoretically that both methods of treating the experimental results to reveal the natural remanent magnetization (NRM) vector are precisely those which algebraically eliminate gyroremanent magnetization (GRM). By implication, the “spurious” remanences found by these and other workers are almost certainly of gyromagnetic origin and not remanences produced as a result of shortcomings in instrumentation. It is further demonstrated that by suitably treating the data obtained by either three‐axis method, GRM can be identified and used to provide information about the anisotropy