The magnetic properties of various R 6 Fe 13Ϫx M 1ϩx compounds (RϭLa, Nd, Gd, and Dy͒ crystallizing in the La 6 Co 11 Ga 3 structure have been investigated by magnetic measurements and x-ray diffraction. It is shown that all Nd 6 Fe 13 M compounds with M ϭAu, Ag, Cu, Si, and Ga order antiferromagnetically around 415 K and evidence is provided that the frequently reported, increase of the magnetization at lower temperature is due to impurities. High-field measurements made at 4.2 K on Nd 6Ϫx Dy x Fe 12.7 Ga 1.3 compounds with xϭ0.0, 0.2, 0.5, and 1.0 show that the R-Fe coupling is not yet broken at 35 T. A large hysteresis in the field dependence of the magnetization is present in all compounds including La 6 Fe 11 Al 3 , indicating the role of the Fe-sublattice anisotropy. A theoretical model for the field dependence of the magnetization is constructed, based on local minimization of the free energy. By taking into account the second-and fourth-order magnetocrystalline anisotropy terms, the magnetization behavior of the compounds, including the large hysteresis, can be explained excellently. A structure of ferromagnetically ordered Fe sheets coupling antiferromagnetically to each other is proposed to explain the experimental data. The hydrides of these compounds are all ferromagnetic ͑light R) or ferrimagnetic ͑heavy R) and have an easy magnetization direction along the c axis due to the Fe-sublattice anisotropy. Their ordering temperatures are near 450 K, just slightly above the Néel temperature of the parent compounds, which can be understood from the proposed spin structure.