Jumonji histone demethylases catalyze removal of methyl marks from lysine residues in histone proteins within nucleosomes. Here, we show that the catalytic domain of demethylase JMJD2A (cJMJD2A) utilizes a distributive mechanism to remove the histone H3 lysine 9 trimethyl mark. By developing a method to assess demethylation of homogeneous, site-specifically methylated nucleosomes, we determined that the kinetic parameters for demethylation of nucleosomes by cJMJD2A are comparable to those of peptide substrates. These findings imply that other domains of the demethylase or its protein partners may contribute to nucleosome recognition in vivo and, in this way, may further regulate demethylation activity and processivity. The quantitative assays of nucleosome demethylation developed in our work provide a platform for future work with complex chromatin substrates and full-length demethylases.