Analytical expressions are derived for both the ${\mathrm{\ensuremath{\pi}}}^{\mathrm{*}}$ and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$ resonances in near-edge x-ray-absorption fine-structure (NEXAFS) spectra from diatomic molecules. A simple criterion is formulated for extracting structural parameters (e.g., the bond lengths) of such molecules from NEXAFS spectra. A universal curve for the positions of resonances is derived from our analytical expressions. The predictions are confirmed by comparisons with computer simulations of NEXAFS spectra for gas-phase ${\mathrm{N}}_{2}$ and ${\mathrm{O}}_{2}$ molecules. \textcopyright{} 1996 The American Physical Society.