In radiometers for the x-ray range (E~10 to 100 keV) the use of oxide scintillators based on gadolinium oxyorthosilicate (GSO) has many advantages over alkali halide scintillators, e.g., NaI(Tl). The shape of spectra obtained with GSO and cadmium tungstate (CWO) scintillators has certain features that substantially increase the sensitivity of radiometers that use the energy windows algorithm and allowed us to design a detector for simultaneous detection of low-energy γ radiation of 241Am (59.6 keV) and 137Cs (≈33 keV). These features of oxide scintillators have allowed a substantial increase in sensitivity of the selective radiometer RK-AG-02M, which is designed for measurements of 241Am activity in soil samples against the background of 137Cs. The results obtained in this work show that the use of GSO and (in several cases) CWO scintillators in instruments involving x-ray range of radiation (e.g., thickness meters, radiometers) is a very promising field for their application. To ensure efficient use of GSO, sufficiently high optical luminescence, scintillation, and other functional characteristics of this scintillator are required, which can be improved by thermal treatment. In this connection, results are presented on thermal treatment of GSO:Ce crystals. In RK-AG-02M we are using a scintillation unit based on a GSO scintillator. To increase the measurement accuracy in the bulk density range of 0.6 to 2.5 g/cm3, a correcting function has been obtained for the radiometer sensitivity.