X-band (~9.45GHz) electron paramagnetic resonance (EPR) spectra of the Kramers ions Er 3 + , Nd 3 + , Yb 3 + and Ce 3 + substituting by about ~1% Y 3 + ions, in yttrium trinitate hexahydrate [Y(NO 3 ) 3 .6H 2 O] and yttrium trisulphate octahydrate [Y 2 (SO 4 ) 3 .8H 2 O] single crystals were recorded at liquid-helium temperatures. Hyperfine EPR transitions were observed for the isotopes of Er, Nd and Yb, except for the Ce 3 + ion which possesses no isotope with non-zero nuclear moment. The spectra indicate the presence of two magnetically- inequivalent R 3 + sites in unit cell in the Y 2 (SO 4 ) 3 .8H 2 O crystal, and one site in Y(NO 3 ) 3 .6H 2 O crystal. The values of the elements of the (anisotropic) g 2 and A 2 tensors were estimated using a rigorous least-squares fitting procedure fitting simultaneously all resonant EPR line positions observed for numerous orientations of the external magnetic field in three mutually perpendicular planes. The absolute signs of the elements of A-matrix and orientations of g- and A-matrices relative to the magnetic axes of the Gd 3 + ion, present naturally as impurity in these crystals, were determined.