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In many applications, multilayer mirrors are exposed to damaging fluences of x rays. In x-ray laser cavities intense optical and broad-band x radiation, from the x-ray laser plasma amplifier, can damage multilayer mirrors on time scales of hundreds of picoseconds. We describe experiments using short duration (500 ps) bursts of soft x rays from a laser produced gold plasma to damage multilayer mirrors designed to reflect wavelengths close to 45 Å at normal incidence. The effect of the damaging x-ray flux on normal incidence reflectivity was time resolved for W/C, WRe/C, WC/C, 303-stainless-steel/C, and Cr3C2/C multilayers. The damage thresholds of the different mirrors were compared, and the Cr3C2/C mirrors were found to be the most resilient. The outer layers of the multilayers were observed to expand slowly as x rays were absorbed, and a more rapid expansion then preceded the total loss of reflectivity, at temperatures well below the melting temperature of the mirror components. It is believed that the dominant expansion mechanism is a change in the amorphous carbon layers to a more graphitic structure. The data are fit quite well by a model that assumes expansion of up to 25% in the thickness of the outermost carbon layers, followed by intermixing of the hotter layers. The rapid expansion has been observed to occur in times from 40 to 150 ps and may be the fastest resolution to date of the phenomenon of graphitization. The integrated reflectivity of the mirrors was observed to increase by up to a factor of 2.5 as they damaged; this reflectivity increase may be consistent with a reduction in the layer roughness.