The gamma-ray and neutron radiation hardness of YBa/sub 2/Cu/sub 3/O/sub 7-x/, Tl/sub 2/Ba/sub 2/CaCu/sub 2/O/sub 8+x/ and Tl/sub 2/Ba/sub 2/Ca/sub 2/Cu/sub 3/O/sub 10+x/ superconducting thin films deposited by off-axis sputtering and laser-ablation deposition techniques on substrates of MgO and LaAlO/sub 3/ was investigated. The unbiased samples were irradiated with 662 keV gamma-rays up to a cumulative dose of 1.5 Mrad(Si) and with neutron nuences up to 1/spl times/10/sup 14/ neutrons/cm/sup 2/. It was determined through nondestructive critical temperature transition, T/sub c/, and critical current density, J/sub c/, measurements and X-ray diffraction analysis that the thin film superconductors were radiation hard up to moderate levels of neutrons and gamma-rays. It was also determined that extended exposure to moderately humid air degraded the critical current density of all the films. >