This paper describes the first observation of persistent spectral hole-burning in actinide-ion-doped crystals. Spectral hole-burning in three zero-phonon lines at 652.1 nm, 658.4 nm and 659.1 nm in SrWO₄:U and one zero-phonon line at 654.4 nm in BaWO₄:U is reported. The holes display quadratic Zeeman shifts. Also when the field is along the (110) direction the holes are split into two indicating the presence of two crystallographically equivalent sites of C₂ symmetry. This is explained in terms of U⁶⁺ ions substituting for W⁶⁺ but having two equilibrium positions displaced in alternate directions along the c axis from the substitutional site. As well as narrow holes there are broad anti-holes, resulting in an unchanged integrated absorption that the hole-burning is photophysical. The mechanism is attributed to the reorientation of the U⁶⁺ between the two sites.