Using the X-ray pulse from the HERMES 11 simulation machine at Sandia National Laboratories, we measured the pulsed radiation-induced attenuation in two optical fibers considered to be "non-rad-hard": the 50-mu-core, graded-index fiber from Corning and the plastic (PMMA) fiber from the Mitsubishi Rayon Company. These fibers were exposed to radiation up to doses of 19.5 and 28 krad(Si), respectively. In addition, fits of their post-radiation recovery were made to the geminate recombination model, from which the recombination-rate and generation constants, characteristic of this theory, were determined. These parameters should be useful in determining the response of the fibers to radiation conditions other than those encountered here.