A series of interstitial ternary nitrides R2Fe17Ny with 2.3<y<2.9 has been prepared for R=Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu and Y. The nitrides have structures related to those of Th2Zn17 or Th2Ni17, but the unit cell volumes are 6-7% greater, and the magnetic ordering temperatures some 400 K higher than for the 2:17 parent compounds. The Fe-Fe exchange interactions are more than doubled by nitrogenation, whereas the R-Fe exchange interactions are little changed. All compounds exhibit easy-plane anisotropy at room temperature, except for Sm2Fe17Ny, which is easy-axis.