The recent detection of both pressure and high-order gravity modes in the classical B-type pulsator Pegasi offers promising prospects for probing its internal structure through seismic studies. To aid further modelling of this star, we present the results of a detailed NLTE abundance analysis based on a large number of time-resolved, high-quality spectra. A chemical composition typical of nearby B-type stars is found. The hybrid nature of this star is consistent with its location in the overlapping region of the instability strips for ß Cephei and slowly pulsating B stars computed using OP opacity tables, although OPAL calculations may also be compatible with the observations once the uncertainties in the stellar parameters and the current limitations of the stability calculations are taken into account. The two known frequencies f1 = 6.58974 and f2 = 0.68241 d-1 are detected in the spectroscopic time series. A mode identification is attempted for the low-frequency signal, which can be associated to a high-order g-mode. Finally, we re-assess the binary status of γ Peg and find no evidence for variations that can be ascribed to orbital motion, contrary to previous claims in the literature.