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The anomalous Hall effect (AHE) is a fundamental spintronic charge-to-charge-current conversion phenomenon and closely related to spin-to-charge-current conversion by the spin Hall effect. Future high-speed spintronic devices will crucially rely on such conversion phenomena at terahertz (THz) frequencies. Here, it is revealed that the AHE remains operative from DC up to 40 THz with a flat frequency response in thin films of three technologically relevant magnetic materials: DyCo5, Co32Fe68, and Gd27Fe73. The frequency-dependent conductivity-tensor elements sigma(xx) and sigma(yx) are measured, and good agreement with DC measurements is found. The experimental findings are fully consistent with ab initio calculations of sigma(yx) for CoFe and highlight the role of the large Drude scattering rate (approximate to 100 THz) of metal thin films, which smears out any sharp spectral features of the THz AHE. Finally, it is found that the intrinsic contribution to the THz AHE dominates over the extrinsic mechanisms for the Co32Fe68 sample. The results imply that the AHE and related effects such as the spin Hall effect are highly promising ingredients of future THz spintronic devices reliably operating from DC to 40 THz and beyond.