Symbiotic stars often exhibit broad wings around Balmer emission lines, whose origin is still controversial. We present the high resolution spectra of the S type symbiotic stars Z Andromedae and AG Draconis obtained with the ESPaDOnS and the 3.6 m Canada France Hawaii Telescope to investigate the broad wings around H$alpha$ and H$beta$. When H$alpha$ and H$beta$ lines are overplotted in the Doppler space, it is noted that H$alpha$ profiles are overall broader than H$beta$ in these two objects. Adopting a Monte Carlo approach, we consider the formation of broad wings of H$alpha$ and H$beta$ through Raman scattering of far UV radiation around Ly$beta$ and Ly$gamma$ and Thomson scattering by free electrons. Raman scattering wings are simulated by choosing an H I region with a neutral hydrogen column density $N_{HI}$ and a covering factor $CF$. For Thomson wings, the ionized scattering region is assumed to cover fully the Balmer emission nebula and is characterized by the electron temperature $T_e$ and the electron column density $N_e$. Thomson wings of H$alpha$ and H$beta$ have the same width that is proportional to $T_e^{1/2}$. However, Raman wings of H$alpha$ are overall three times wider than H$beta$ counterparts, which is attributed to different cross section for Ly$beta$ and Ly$gamma$. Normalized to have the same peak values and presented in the Doppler factor space. H$alpha$ wings of Z And and AG Dra are observed to be significantly wider than H$beta$ counterpart, favoring the Raman scattering origin of broad Balmer wings.
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