The neutron capture cross sections of 241Am and 243Am to the ground and isomeric states of 242Am and 244Am have been calculated using the Hauser-Feshbach statistical theory of nuclear reactions for energies from thermal to 2 MeV. The parameters for the calculations were obtained from recent data on (241Am + n) and (243Am + n) or, where necessary, from systematics of actinide nuclei. The calculated values are in good agreement with the sparse experimental data.