The magnetic properties of the R2Fe14BHx (R = Gd, Pr, and Dy) compounds have been studied by measuring low-field ac magnetic susceptibility vs temperature and magnetization vs temperature and applied magnetic field on magnetically aligned samples. A strong reduction in the magnetocrystalline anisotropy of the Gd-based compounds is observed, and the compounds remain axial in the measured temperature range. A hydrogen induced spin reorientation transition (HISRT) takes place in the Dy2Fe14BHx series for x greater than or equal to 1, with the transition temperature T-s increasing with increasing hydrogen content. In the Pr2Fe14BHx compounds no HISRT is Found. however for 0<x less than or equal to 3 we observe first-order magnetization processes (FOMP), with the critical field H-e decreasing with increasing hydrogen content. For the Pr2Fe14BH5.5 compound the reduction is so strong that H(c)approximate to 0, and the compound remains in a conical phase in the studied temperature range (5 - 470 K). We have combined analytical methods and a crystalline electric field-mean field model to obtain a quantitative evaluation of the effect of hydrogenation on the magnetic and crystal-field interactions. We have found that the observed behavior in the Gd, Dy, and Pr series can be explained by a decrease of the Fe sublattice anisotropy and by a decrease (in the Dy and Pr series) of the crystal-field parameters B-n0 (n=2, 4, and 6) under hydrogenation. The hydrogen induced Variations of the R-Fe exchange interaction seem to have a minor influence on the observed magnetic behavior.