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We have measured the conductivity induced in films of polyethylene, epoxy, polytetrafluoroethylene, polyethylene terephthalate, polyimide, and glass by x rays at dose rates between 109 and 1010 rad/sec (dose in air). The films were 0.05 to 1.25 mm thick. The x-ray spectrum peaked in the vicinity of 10 keV, and the x-ray pulse width was about 40 nsec FWHM. X-ray induced photocurrents were found to obey Ohm's law at low bias voltages (less than 1 kV). Above 1 kV, however, we observed that the peak photoconductivity signals from some of the 0.05-mm-thick materials began to increase at a slightly faster than linear rate with bias voltage. The glass samples exhibited no apparent delayed conductivity, while the other sample materials showed various amounts. The magnitude of the delayed conductivity in polytetrafluoroethylene, polyethylene terephthalate, and polyimide depended on the electric field, an effect that is consistent with Poole-Frenkel field assisted carrier generation. We have qualitatively described the magnitude and time dependence of the conductivity signals by a simple trapping model, using reasonable values for mobility, trap density, capture cross sections and trap depths.