The observation of C-H bending, and C-C and C-H stretching vibrational levels in high-resolution C 1s-1π* photoabsorption spectra of ethylene and benzene demonstrates that, within the validity of the Franck-Condon principle, both molecules have broken symmetry in this core-excited state. A simple model based on the antibonding character of the π* electron, and on the local rehibridization of the bonding orbitals on the excited C atom, is utilized to explain our observations and to show that both core-excited molecules become nonplanar. Our results also show that the core hole is localized on the excited carbon atom.