Neutron-diffraction measurementswere performed on polycrystalline samples of 13 different compounds of the type RM2X& (R, a heavy lanthanide from Gd to Tm; M, the 3d element Fe, Co, Ni, or Cu', X, Si or Ge}, at room temperature and at low temperatures. The crystallographic structure of these compounds belongs to the tetragonal space group I4/mmm (D4q ). It was found that these compounds, paramagnetic at room temperature, undergo a transition to antiferromagnetism at low temperatures.The transition temperatures and most of magnetic structures were determined. Below the transition temperature, magnetic ordering was found only on the R sublattice, and no magnetic ordering was detected on the M sublattice. The magnetic lattices were found to be characterized by propagation vectors of k=(0, 0, 1} in the cobalt compounds investigated (TbCo2Si2, HoCo2Si2, DyCo2Ge2, and ErCo&Ge2), k = (~,0, 2 ) in the copper compounds investigated (TbCu2Si2, HoCu2Si» TbCu2Ge2, and HoCu2Ge2), and incommensurate k =(0,0,0.76) in HoNi2Geq (unsolved incommensurate in other nickel compounds and in iron compounds). Together with previously published results on other RM2X2 compounds, the magnetic lattice is found to vary with M and be almost invariant to R.