Abstract In a can-annular gas turbine combustion system, low-frequency self-excited combustion instabilities can arise from coupled interactions between adjacent can combustors, rather than from individual combustors. These interactions—in either a push–push or a push–pull mode – are caused by the presence of a cross-talk area upstream of the first stage turbine stator vanes. The mechanisms governing the selection and growth of the interaction modes are not well understood, particularly for systems with multiple oscillators (combustors). Here we describe experimental observations of mutual synchronization between two coupled-combustors, each containing a lean-premixed swirl-stabilized turbulent flame, subjected to symmetric and asymmetric inlet boundary conditions. Our results reveal that when two combustors oscillating at different natural frequencies are connected via a cross-talk area, they can become mutually synchronized with each other, exhibiting global oscillations at a common frequency. The presence of cross-talk communication can excite strong oscillations in the coupled dual-combustor system, even when each combustor is individually stable in isolation. By contrast, for certain asymmetric inlet boundary conditions, coupling the two combustors together stops them from oscillating completely, even though each combustor in isolation oscillates in a large-amplitude limit cycle. In nonlinear dynamics, such mode suppression is known as amplitude death and is a classical feature of coupled self-excited oscillators, with potentially wider applications for passive control of combustion instabilities. We analyze a large set of experimental data in non-dimensional domains, and demonstrate that the coupled mode is not defined by the phase difference between the heat release rate oscillations of the two combustors, but rather by the phase difference between their acoustic pressure fluctuations. Mode selection is found to be strongly correlated to the degree of asymmetry in the magnitude of the flames' heat release rate oscillations in adjacent combustors. As well as providing the first experimental evidence of amplitude death in a combustion system, this study reveals a previously unrecognized role of combustor-to-combustor interactions in provoking self-excited combustion instabilities in multiple-combustor gas turbine systems.