Ni-oxide-based thin films, prepared by sputtering, are investigated by electrochemical impedance spectroscopy in a KOH electrolyte. The films are electrochromic, and an increase of the applied potential leads to a variation from a bleached to a colored state as a result of proton (H+) extraction together with extraction of electrons from the valence band. The complex frequency-dependent impedance displays different features in different potential ranges. At low potentials, where coloration is weak, the spectra give evidence for a constant-phase element in parallel with a leak resistance. At intermediate and high potentials, the impedance spectra indicate the presence of a diffusion process, and a model for anomalous diffusion gives excellent fits to the spectra except in a crossover region. The applicability of this model in a significant part of the studied potential range suggests the presence of a multiple-trapping process for the ions. The potential dependence of the chemical capacitance, as well as the diffusion coefficient of un-trapped ions, are analyzed. The electrochemical density-of-states of the charge-compensating electrons gives indications of the top of the valence band and of a band tail extending into the band gap. Diffusion coefficients are found to increase steeply in the crossover potential region to very high values at high potentials. These features are discussed and related to the electrochromic behavior of Ni-oxide-based thin films.