Reproduction of quasi-biennial oscillations (QBO) and semiannual oscillations (SAO), as general features of equatorial stratospheric circulation, are considered for atmospheric general circulation model unit (AGCM) of INM RAS climate model. The general problem of QBO representation in AGCMs and particularly in INM RAS AGCM and the key physical processes which define QBO and SAO characteristics are considered. QBO and SAO long-term response to anthropogenic forcing and also their sensitivity to other global atmospheric processes are studied based on the modelling results by new versions of INM AGCM model (with high spatial resolution and hybrid vertical coordinate, 2°x2.5° and 80 vertical levels, altitudes are 0-90 km) and INMCM5 climate model (resolution for atmospheric unit 1°x1.25° and 128 vertical levels, altitudes are 0-60 km). It is shown that QBO period and phase structure in these models are highly sensitive to global atmospheric characteristics change and could be considered as a fingerprint of system instability, herewith the nonlinear response of QBO structure is quantified. The synchronization of QBO and SAO is identified and also could play a crucial role in long-term QBO variability.