The local atomic structure of Co, Fe, and Ce in aluminum-rich amorphous alloys of ${\mathrm{Al}}_{100\mathrm{\ensuremath{-}}2\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$ (x=8, 9, and 10) and Ce in ${\mathrm{Al}}_{80}$${\mathrm{Fe}}_{10}$${\mathrm{Ce}}_{10}$ has been investigated by x-ray-absorption fine structure (XAFS) spectroscopy. The materials, 1- and 3-\ensuremath{\mu}m-thick films, were prepared by vapor quenching using the dc magnetron sputtering method. We show that the composition of the glass-forming region of these magnetron-sputtered alloys strictly follows the theoretical limit calculated on the basis of the atomic size criterion. From analyses of the XAFS data at the K edges of Co and Fe and the ${\mathit{L}}_{3}$ edge of Ce, the following conclusions with regard to local structure are made. The first coordination sphere of Co in ${\mathrm{Al}}_{100\mathrm{\ensuremath{-}}2\mathit{x}}$${\mathrm{Co}}_{\mathit{x}}$${\mathrm{Ce}}_{\mathit{x}}$ (x=8, 9, and 10) consists of 5.8 to 6.4 Al atoms at a distance of 2.44 \AA{}. The local coordination sphere for Fe in ${\mathrm{Al}}_{80}$${\mathrm{Fe}}_{10}$${\mathrm{Ce}}_{10}$ consists of 6.4 Al atoms at a distance of 2.47 \AA{}. Ce in both systems appears to be coordinated with roughly 5 and 9 Al atoms at distances of 2.95 and 3.15 \AA{}, respectively. These results are discussed in light of the dense random packing (DRP) of hard spheres model. Both Co-Al and Fe-Al bond lengths are anomalously short (9 and 8 % contraction, respectively) with also anomalously low coordination numbers (45% reduction) from values based on the DRP model using the metallic state radii.These anomalous changes indicate a strong interaction between Co or Fe atoms and the Al atoms which perhaps may be a result of a covalently bonded environment. The Ce-Al distance in both the Al-Co-Ce and Al-Fe-Ce systems, on the other hand, is smaller by only 0.17 \AA{} (a contraction of only 5%) and the coordination number is reduced by only 13% from expected values based on the DRP model. The contraction in the distance and reduction in the coordination number for Ce are much smaller than those values of the Co or Fe and, hence, the local bonding for Ce is likely to be metallic in character.