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The structure of genuine and conjugate Fermi holes in two-electron atomic systems, namely He and He-like atomic ions, has been studied relying on accurate full configuration interaction wave functions. The standard Fermi hole exists in the vicinity of region in the two-electron coordinate space satisfying the well-known condition, r1 = r2, while the conjugate Fermi hole exists in the vicinity of region close to this genuine Fermi hole but satisfying r¹ = r2 instead of r1 = r2. Existence of these holes has shown to give an insightful interpretation of the origin of the first Hund rule and of the anomalously strong angular correlation manifested in the series of the singlet-triplet pair of singly-excited states of the aforementioned systems. [ABSTRACT FROM AUTHOR]