The low-frequency dielectric response of hole-doped insulators La2Cu1−xLixO4 and La2−xSrxNiO4 shows a large dielectric constant ε ′ at high temperature and a step-like drop by a factor of 100 at a material-dependent low temperature T f . T f increases with frequency and the dielectric response shows universal scaling in a Cole-Cole plot, suggesting that a charge glass state is realized both in the cuprates and in the nickelates.Charge inhomogeneities in hole-doped oxides attract great interest, in part due to their possible relation to high temperature superconductivity. Perhaps the best known examples are stripes, wherein holes congregate along lines which serve as domain boundaries in a surrounding antiferromagnetic environment. These were predicted [1,2] and observed in Nd-doped La 2−x Sr x CuO 4 [3] and in hole-doped, but insulating nickelates [4,5,6]. Inhomogeneities in these complex oxides are naturally linked to the competition between myriad interactions (e.g. Coulomb, kinetic, magnetic, strain,...). The resulting compromise amongst these is non-uniform structures [1,2] and experimental evidence for glassiness [7,8]. Theoretically, the non-uniform nature of these states easily allows for the proliferation of many metastable and low lying states. In accord with this intuition, replica calculations [9, 10] indeed suggest an exponentially large number of metastable states built from these rich non-uniform domains. This proliferation of metastable states allows, in principle, for a glass to naturally emerge. As spin and charge degrees of freedom are intertwined, glassy signatures and inhomogeneities in the spin sector naturally suggest analogous effects in the charge channel-nonuniform charge distributions should appear.In this Letter, we report the first observation of sharp dielectric anomalies both in the cuprates and nickelates. The low-frequency dielectric constants of La 2 Cu 1−x Li x O 4 (x ≈ 0.023) and La 2−x Sr x NiO 4 (x = 1/3) show a frequency-dependent drop from a large dielectric constant ε ′ , of order 10 4 , at high temperatures to a modest value (10 2 ) below a temperature T f . A phenomenological Davidson-Cole plot [11], commonly used to analyze classical structural glasses [11,12], successfully captures the dielectric behavior which shows universal scaling. The characteristic relaxation time obtained from the analysis shows a polynomial temperature dependence with a finite glass transition temperature T 0 , which is consistent with glassy charge dynamics arising from a collective behavior of doped holes both in the cuprates and in the nickelates.The Li-doped lanthanum cuprate La 2 Cu 1−x Li x O 4 crystals were prepared by flux growth and the Sr-doped lanthanum nickelate La 2−x Sr x NiO 4 was grown by the floating zone method [13]. For dielectric measurements, an Al 2 O 3 layer of 1000Å was deposited between the sample and metal contacts to prevent a polarization of charge at an electrode/sample interface that can produce a spurious dielectric response. Extensive tests were made to ensure th...