The title compounds were prepared from the elements by reactions in sealed tantalum tubes in a water-cooled sample chamber of a high-frequency furnace. They crystallize with the ZrNiAl-type structure, space group P2m. The structures of the cerium compounds were refined from single-crystal x-ray diffraction data: a = 767.3(1) pm, c = 410.37(4) pm, wR2 = 0.0324, 521 F²-values for CePdMg; a = 755.02(7) pm, c = 413.82(4) pm, wR2 = 0.0393, 514 F²-values for CePtMg; and a = 774.1(3) pm, c = 421.6(1) pm, wR2 = 0.0355, 395 F²-values for CeAuMg, with 14 variables for each refinement. The palladium compound shows a small homogeneity range: CePd_1+xMg_1-x. The structures contain two crystallographically different transition metal sites T1 and T2 which are located in tri-capped trigonal prisms: [T1 Mg₆Ce₃] and [T2 Ce₆Mg₃]. Magnetic susceptibility and heat capacity measurements reveal long-range magnetic ordering at 2.1(2) K for CePdMg, 3.6(2) K for CePtMg, and 2.0(2) K for CeAuMg. Curie-Weiss behaviour at higher temperatures shows that the cerium ions are in the 3+ oxidation state. The isotypic LaTMg compounds are Pauli paramagnetic down to lowest temperatures (T = 0.3 K). All the compounds, RETMg (RE = La, Ce; T = Pd, Pt, Au) show metallic behaviour.