The present work focuses on the study of the resonance and coupling of an underexpanded circular twin-jet system operating at a nozzle pressure ratio of $5.0$. Particle image velocimetry data from previous work were revisited, and a symmetry-imposed proper orthogonal decomposition (POD) was performed. It is shown that the system is dominated by a single POD mode pair symmetric about the internozzle plane, and the resonance loop is modulated by a third POD mode related to shear thickness modulation. A spatial Fourier transform of the leading POD mode pair leads to the identification of the peak wavenumbers and radial shapes of the different waves at play in the screech phenomenon. Locally parallel linear stability analysis around the experimental mean flow is also performed, in order to provide clarification of the mode ‘locking’ mechanism, i.e. the selection of the global mode associated with screech. It is shown that the characteristics of the Kelvin–Helmholtz wavepackets alone are not sufficient to explain the coupling observed in the experimental data. A consideration of the upstream-travelling guided jet mode offers an explanation; only specific symmetries of upstream modes can be supported in the frequency range at which resonance occurs. Results from stability analysis point to structures at frequencies and wavenumbers close to those found experimentally, and their spatial structures show excellent agreement with the POD modes. The present results suggest that the resonance loop is closed by an upstream-travelling guided jet mode for the twin-jet system at high nozzle pressure ratio.