The results of studies of Y$_{2}$Ti$_2$O$_7$ single crystals doped with Er$^{3+}$ and Yb$^{3+}$ ions by means of electron paramagnetic resonance (EPR) and dc-magnetometry are reported. EPR signals of the trigonal centers with the characteristic hyperfine structure of Er$^{3+}$ or Yb$^{3+}$ ions were observed. Field dependences of magnetization of single crystals for magnetic fields directed along the crystallographic axes and temperature dependences of magnetic susceptibilities were measured. Spin Hamiltonian parameters ($g$-factors and parameters of the hyperfine interaction) for Er$^{3+}$ and Yb$^{3+}$ ions were obtained from analysis of experimental data. The registered EPR spectra and magnetization curves were successfully reproduced by simulations in framework of the crystal-field approach, in particular, with an account for hybridization of ground 4f$^{13}$ configuration of Yb$^{3+}$ ions with the charge transfer states.
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