We report transient radiation-induced effects on solid core microstructured optical fibers (MOFs). The kinetics and levels of radiation-induced attenuation (RIA) in the visible and near-infrared part of the spectrum (600 nm-2000 nm) were characterized. It is found that the two tested MOFs, fabricated by the stack-and-draw technique, present a good radiation tolerance. Both have similar geometry but one has been made with pure-silica tubes and the other one with Fluorine-doped silica tubes. We compared their pulsed X-ray radiation sensitivities to those of different classes of conventional optical fibers with pure-silica-cores or cores doped with Phosphorus or Germanium. The pulsed radiation sensitivity of MOFs seems to be mainly governed by the glass composition whereas their particular structure does not contribute significantly. Similarly for doped silica fibers, the measured spectral dependence of RIA for the MOFs cannot be correctly reproduced with the various absorption bands associated with the Si-related defects identified in the literature. However, our analysis confirms the preponderant role of self-trapped holes with their visible and infrared absorption bands in the transient behaviors of pure-silica of F-doped fibers. The results of this study showed that pure-silica or fluorine-doped MOFs, which offers specific advantages compared to conventional fibers, are promising for use in harsh environments due to their radiation tolerance.