A γ -spectrometer facility operating in the βγ coincidence mode is able to detect ultralow activities of 131 m ïÂ, 133 m ïÂ, 133 ï , and 135 Xe isotopes. A gas sample is introduced into the measuring chamber that is a thin-walled aluminum cylinder with its inner surface coated with organic scintillator to detect β particles and conversion electrons. The chamber is placed in the well of a NaI(Tl) crystal detector of X and γ rays. The resultant γ -ray spectrum is formed by extracting X-and γray pulses coincident in time with pulses of β particles and conversion electrons. The radiation background level is thereby reduced by two orders of magnitude in comparison with measurements in the standard mode (without coincidences), which leads to a significant increase in the spectrometer sensitivity. The design for the measuring system used in the Äêàäë-01 complex of equipment is described, along with the determination of its efficiency and its energy calibration. Data on the sensitivity achieved are presented.