Magnetization measurements along the main symmetry directions of the tetragonal structure, [100], [110] and [001], have been performed on several single crystals (R = Y, Tb and Ho), at applied high magnetic fields up to 12 Tesla and temperatures ranging from 4.2 to 300 K. From the measurements on the yttrium compound the second- and fourth-order anisotropy constants and the spontaneous magnetization of the Fe sublattice have been determined. The complex magnetic behaviour has been explained using a single-ion model for the crystal electric field (CEF) interaction and a mean-field model for the exchange interaction. A reliable set of CEF parameters and mean exchange field have been obtained for the and intermetallic compounds. All the experimental features observed, the first-order magnetization process under magnetic field in and spin reorientation transition (SRT) in , have been explained using such CEF and exchange parameters. A study of the character of the SRT observed in the intermetallic compound has been undertaken by measuring the parallel and perpendicular components of the magnetization to the applied magnetic field. The experimental results obtained have been explained considering the coexistence of two magnetic phases for temperatures close to the spin reorientation one.