X-ray-absorption fine structure (XAFS) above the Fe K edge, the Ce $L_3$ edge, and the Al K edge in amorphous ${\mathrm{Al}}_{90}{\mathrm{Fe}}_x{\mathrm{Ce}}_{10-x}$ $(x=3,$ 5, and 7) alloys have been measured and analyzed. Quantitative analyses of the Fe K-edge and Ce $L_3$-edge extended XAFS spectra are limited to local structure parameters of the first coordination sphere. Comparison of experimental x-ray-absorption near-edge structure (XANES) spectra with theoretical multiple-scattering (MS) XANES spectra for model compounds, such as crystalline ${\mathrm{FeAl}}_6$ and ${\mathrm{CeAl}}_4,$ allows one to determine the local structure around the aluminum, iron, and Ce sites in ternary amorphous alloys. Using the theoretical MS approach, we show that the Fe and Al K-edge XANES are sensitive to the structure of coordination spheres, which extend up to nearly 4.4 and 3.3 Å, respectively. The Ce $L_3$-edge XANES, on the other hand, is sensitive to the structure that extends up to 3.15 Å.