At the recently built FLASH x-ray free-electron laser, we studied the reflectivity of Si/C multilayers with fluxes up to 3 x 10(14) W/cm2. Even though the nanostructures were ultimately completely destroyed, we found that they maintained their integrity and reflectance characteristics during the 25-fs-long pulse, with no evidence for any structural changes over lengths greater than 3 A. This experiment demonstrates that with intense ultrafast pulses, structural damage does not occur during the pulse, giving credence to the concept of diffraction imaging of single macromolecules.