The title compounds were synthesized by reacting the elements in sealed tantalum tubes in a high-frequency furnace. They were investigated by X-ray di4raction on both powders and single crystals. With the trivalent rare earth elements they adopt the ZrNiAl-type structure, space group P6 2m: a ؍ 782.5(3) pm, c ؍ 432.8(1) pm, wR2 ؍ 0.0420, and 277 F 2 values for CeAgMg and a ؍ 775.7(3) pm, c ؍ 426.1(1) pm, wR2 ؍ 0.0387, and 271 F 2 values for NdAgMg with 15 parametm ers for each re5nement. Geometrical motifs in CeAgMg are two types of silver-centered tricapped trigonal prisms: [Ag1Mg 3 Ce 6 ] and [Ag2Mg 6 Ce 3 ]. The silver and magnesium atoms form a three-dimensional [AgMg] network in which the cerium atoms 5ll distorted hexagonal channels. With divalent europium and ytterbium the orthorhombic TiNiSi-type occurs, space group Pnma: a ؍ 777.4(2) pm, b ؍ 463.0(1) pm, c ؍ 898.8(2) pm, wR2 ؍ 0.0430, and 401 F 2 values for EuAgMg and a ؍ 753.66(7) pm, b ؍ 446.49(7) pm, c ؍ 887.2(1) pm, wR2 ؍ 0.0742, and 485 F 2 values for YbAgMg with 21 parameters for each re5nement. The europium(ytterbium) and magnesium atoms form zigzag chains of edge-and face-sharing trigonal prisms which are centered by the silver atoms. Also in EuAgMg and YbAgMg a three-dimensional [AgMg] network occurs in which the europium(ytterbium) atoms are embedded. The magnesium positions of the cerium, neodymium, europium, and ytterbium compound show a small mixed magnesium/silver occupancy, leading to the re5ned compositions CeAg 1.034(7) Mg 0.966(7) , NdAg 1.035(6) Mg 0.965(6) , EuAg 1.032(6) Mg 0.968(6) , and YbAg 1.053(8) Mg 0.947(8) for the crystals investigated. The crystal chemistry and chemical bonding in these intermetallics is brie6y discussed.