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The high-field magnetization process in the hydrogen-charged R2Fe17H3 (R=Tb , Dy, Ho and Er) single crystals is studied along principal crystallographic directions at T=4.2 K and compared with that of the known parent R2Fe17 compounds. Substantial changes of the magnetic anisotropy behavior induced by hydrogenation are found. Depending on the rare earth atom, the R2Fe17H3 compounds possess the “easy-axes”, “easy-cone” and “easy-plane” types of magnetocrystalline anisotropy (MCA), whereas the precursors R2Fe17 have the easy-plane type of MCA only. The various observed types of the field-induced phase transitions in R2Fe17H3 are discussed and information on the effect of hydrogen on the strength of R-Fe coupling is obtained.