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[en] The purpose of this paper is to characterise and model the A1 and A2 screech modes in supersonic jets operating at off-design conditions. The usual screech-modelling scenario involves a feedback loop between a downstream-travelling Kelvin–Helmholtz instability wave and an upstream-travelling acoustic wave. We review state-of-the-art screech-frequency prediction models and associated limitations. Following the work of Edgington-Mitchell et al. (J Fluid Mech 855, 2018), a new prediction approach is proposed where the feedback loop is closed by the upstream-travelling jet modes first discussed in Tam and Hu (J Fluid Mech 201:447–483, 1989) in lieu of the free-stream sound waves. The Kelvin–Helmholtz and upstream-travelling jet modes are obtained using a cylindrical vortex-sheet model. The predictions provide a better agreement with experimental observations than does the classical screech-prediction approach. Screech dynamics associated with the staging process is explored through a wavelet analysis, highlighting that staging involves mutually exclusive switching that is underpinned by non-linear interactions. Graphical abstract: .