The exchange splittings of the ytterbium ground-state doublet and of an excited state ($J=\frac{5}{2}$) doublet have been determined from spectroscopic studies of single-crystalline, ytterbium-iron garnet. The splittings were observed at 77\ifmmode^\circ\else\textdegree\fi{}K as a function of the orientation of the magnetization of the crystal. The splittings exhibit the functional form of the $g$ tensor of a two-level system. The principal values of the splittings (referred to local $x$, $y$, $z$ axes) are, for the ground state doublet, 11.6, 25.7, and 29.9 ${\mathrm{cm}}^{\ensuremath{-}1}$ and, for the excited state doublet, 15.9, 5.8, and 29.9 ${\mathrm{cm}}^{\ensuremath{-}1}$.From the ground state splitting, using $g$ values for ytterbium in yttrium gallium garnet, the approximate principal values of the exchange field (assumed to act on the ytterbium spin magnetic moment only) were found to be 349 000 gauss, 611 000 gauss and 678 000 gauss. The principal values of the effective field (assumed to act on the total magnetic moment) are one fourth as large as those of the exchange field.On the basis of the ground state exchange splitting, calculations of various macroscopic properties of ytterbium-iron garnet, as a function of orientation of magnetization and of temperature, have been carried out by others. The calculated properties are in generally good agreement with experiment, but the sharp, low-temperature magnetic anisotropy anomalies which have been observed in ytterbium-doped yttrium iron garnet are not explained by the spectroscopic data.