The Mössbauer spectra of CeFe11Ti and CeFe11TiH obtained between 4.2 and 295 K are analysed in terms of the model used to analyse the spectra of the RFe11Ti and RFe11TiH compounds, where R is Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er and Lu. The hyperfine parameters obtained with a consistent model that considers both the easy magnetization direction and the titanium preferential site occupancy are discussed as a function of rare-earth atomic number, temperature and hydrogen content. The average hyperfine fields in the RFe11Ti and RFe11TiH compounds are described with a two-sublattice model in which the iron sublattice contributions coincide with the fields observed in LuFe 11Ti and LuFe11TiH, respectively. In both series, the rare-earth sublattice contributes a transferred field which occurs as a result of indirect exchange between the rare-earth 4f and iron 3d electrons and depends on the nature of the rare-earth element. The increase in average hyperfine field and isomer shift upon hydrogenation of the RFe11Ti compounds results from the unit-cell expansion upon hydride formation. The observed average quadrupole shift is closely related to the magnetic anisotropy exhibited by each compound.