The rare-earth-hydrogen systems possess phase diagrams with rather extended solid solution (alpha -RHx) and dihydride (beta -RH2+x) regions, leading eventually - for high enough concentrations and low enough temperatures - to ordering interactions between the x-hydrogens. In the case of magnetic Rs, this gives rise to a multitude of fascinating phenomena caused by the competition between magnetic anisotropy and RKKY interactions, on the one hand, and the H-sublattice (via the crystal field), on the other. Thus, in the beta -RH2+x-phase, the excess x-hydrogens occupying the octahedral sites of the CaF2-type dihydride lattice often order in a tetragonal sublattice, of DO22 symmetry corresponding to a RH2.25 stoichiometry. This strongly modifies the various coexisting and/or overlapping commensurate and incommensurate magnetic structures present, sometimes leading to their complete disappearance or to the appearance of magnetic short-range order. Recent neutron-scattering results obtained on the systems RH(D)(2+x), with R = Tb, Dy, Ho, are given as an illustration. (C) 2001 Elsevier Science BY All rights reserved.