Cubic Y$_{2}$Ti$_{2}$O$_{7}$ single crystals doped with Er$^{3+}$ and Yb$^{3+}$ ions have been studied by the methods of electron spin resonance (ESR) and selective laser spectroscopy. ESR spectra exhibit signals from rare-earth ions that substitute for yttrium ions in sites with local trigonal symmetry. The $g$ tensor components are determined. The results of optical investigations indicate that impurity centers of several types are formed; the sublevel energies of the ground and excited multiplets of these centers are found. Among the great variety of detected optical centers, the centers that dominate in the formation of ESR spectra are discriminated. An analysis of the experimental data using the exchange-charge model have made it possible to determine the sets of parameters of the crystal field for Er$^{3+}$ and Yb$^{3+}$ ions substituting Y$^{3+}$ ions in regular crystallographic sites in pyrochlore Y$_{2}$Ti$_{2}$O$_{7}$.
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