We have studied the magnetic properties and decomposition behaviour of various ternary nitrides of the type R2Fe17N2.7 with R = Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu and Y. The magnetic anisotropy of the R2Fe17N2.7 compounds was studied on magnetically aligned powders in field strengths up to 35 T. The rare-earth sublattice anisotropy is much stronger in R2Fe17N2.7 than in R2Fe17, leading to an easy c-axis anisotropy in Sm2Fe17N2.7. For Er2Fe17N2.7 and Tm2Fe17N2.7 spin-reorientation transitions were observed upon cooling from room temperature, starting at about 150 and 225 K, respectively. The intersublattice-coupling strength between the R- and Fe-sublattice magnetization was found to remain approximately unaltered after charging R2Fe17 with nitrogen gas.