The rare earth double tungstates are investigated recently by different experimental techniques, because they are very perspective materials for the stimulated light generation in over a wide range of frequencies. The common scheme of the laser generation channels for the majority rare earth ions in tungstates matrix was presented in work [1]. The α-КRE(WO4)2 tungstate has also the sufficiently large optical nonlinearity to be used in the devices working on the basis of the Raman effect [2, 3]. The double tungstate reveal an interesting properties at low temperature. For the first time in so low symmetry crystals the structural ordering phase transitions connected with cooperative Jahn-Teller effect were observed [4, 5]. Until now, the EPR spectra of the Gd 3+ [6], Dy 3+ [7], Er 3+ [8], Nd 3+ [9] and Yb 3+ [10] ions in the magnetically diluted and concentrated double tungstate single crystals have been investigated.figureFig.1. EPR spectrum of the Nd 3+ ion in KY(WO4)2 for the z-orientation (В||z). The experimental spectrum is shown on the top of the figure.The electron paramagnetic resonance (EPR) of Nd 3+ ion in KY(WO4)2 single crystal was investigated at T=4.2 K using X-band spectrometer. The resonance absorption observed on the lowest Kramers doublet represents the complex superposition of three spectra, that correspond to the neodymium isotopes with different nuclear moments. Thus, in the monoclinic doped by Nd 3+ ion KY(WO4)2 single crystal strong magnetic anisotropy is observed. Its manifests itself in significant difference of both principal values of the g-tensor and hyperfine splitting tensor, as well as in the nonequdistance of the hyperfine structure lines, which is strongly pronounced in the x and y orientations. The parameters of the spin Hamiltonian and directions of the main axes of the g-tensor with respect to the crystallographic axes were determined. The broadening of the resonance lines with increasing temperature is connected with short times of the spin-lattice relaxation, caused by processes of the resonance fluorescence of the phonons (the Orbach-Aminov process). The low temperature dependence of the g-factor is caused by the presence of the strong spin-orbital and orbital-lattice couplings. This phenomena is characteristic for ions with unquenched orbital moment.