The hydrogenation properties of Laves phases LnMg (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Ho, Er, Tm, Yb) were investigated by thermal analysis, X-ray, synchrotron, and neutron powder diffraction. At 14.0 MPa hydrogen gas pressure and 393 K, PrMg and NdMg take up hydrogen and form the colorless, ternary hydrides PrMgH (P422, a = 632.386(6) pm, c = 945.722(11) pm) and NdMgH (P422, a = 630.354(9) pm, c = 943.018(16) pm). The crystal structures were refined by the Rietveld method from neutron powder diffraction data on the deuterides (PrMgD, P422, a = 630.56(2) pm, c = 943.27(3) pm; NdMgD, P422, a = 628.15(2) pm, c = 940.32(3) pm) and shown to be isotypic to LaMgD. The LaMgD type of hydrides decompose at 695 K (La), 684 K (Ce), 684 K (Pr), 672 K (Nd), and 639 K (Sm) to lanthanide hydrides and magnesium. The Laves phase EuMg forms a hydride EuMgH of black color. Its crystal structure (P222, a = 664.887(4) pm, b = 1136.993(7) pm, c = 1069.887(7) pm) is closely related to the hexagonal Laves phase (MgZn type) of the hydrogen-free parent intermetallic. GdMg and TbMg form hydrides GdMgH with orthorhombic unit cells (a = 1282.7(4) pm, b = 572.5(2) pm, c = 881.7(2) pm) and TbMgH (a = 617.8(3) pm, b = 1045.8(8) pm, c = 997.1(5) pm), presumably also with a distorted MgZn type of structure. CeMgH and NdMgH are paramagnetic with effective magnetic moments of 2.49(1) μ and 3.62(1) μ, respectively, in good agreement with the calculated magnetic moments of the free trivalent rare-earth cations (μ(Ce) = 2.54 μ; μ(Nd) = 3.62 μ).