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Cross sections for the ¹⁰⁹Ag(n,2n)^108mAg reaction are measured using an activation method relative to cross sections for the ⁹³Nb(n, 2n)^92mNb reaction in the 13.64- to 14.80-MeV neutron energy range. Values of 223 ± 7, 233 ± 18, 227 ± 20, 224 ± 18, 232 ± 8, and 236 ±7 mb are obtained, respectively, at neutron energies of 13.64, 13.79, 14.03, 14.33, 14.60, and 14.80 MeV. The neutron energies in these measurements are determined by cross-section ratios for ⁹⁰Zr(n,2n)^89m+gZr and ⁹³Nb(n,2n)^92mNb reactions.