The presence of global hydrodynamic instability (GHI) in turbulent premixed flames has been shown to reduce the sensitivity of heat-release-rate (HRR) responses to external acoustic forcing, suggesting that GHI could passively weaken thermoacoustic oscillations detrimental to combustion systems. This study adopts a mutual synchronization approach to investigate the coupled interactions between a bluff-body stabilized turbulent premixed flame containing GHI and the acoustic modes of its surrounding combustor. In the absence of external forcing, flame HRR oscillations and combustor acoustic modes can mutually synchronize , but the impact of mutual synchronization on resulting flame response or acoustic pressure amplitude remains unclear. Therefore, this study systematically investigates mutual synchronization, its dynamical states, and subsequent flame response/acoustic pressure amplitude using temporal and spatial analysis. Simultaneous CH* chemiluminescence imaging and unsteady pressure measurements were conducted in a bluff-body stabilized lean-premixed turbulent combustor. By increasing the combustor length (1200 mm ⩽ L ⩽ 2700 mm) while maintaining a fixed equivalence ratio (ϕ = 0.65) and Reynolds number (Re = 10785), four distinct flame modes were observed: (i) a self-sustained vortex shedding mode due to GHI at L = 1200 mm, also known as the hydrodynamic mode; (ii) a self-sustained 1 combustor mode due to thermoacoustic instability at L = 1700 mm; (iii) a hybrid mode at L = 2500 mm, where both the GHI and thermoacoustic modes coex-ist; and (iv) a mutually synchronized mode at L = 2700 mm, where GHI and thermoacoustic modes are locked into each other. Temporal analysis reveals the coexistence of various dynamical states during mutual synchronization, including a simultaneous increase in the amplitudes of flame HRR and acoustic pressure oscillations. Similarly, spatial analysis reveals strong HRR fluctuations occurring at the recirculation zone due to large-scale vortex roll-up. Lastly, two distinct mechanisms causing flame blowoff are identified: (i) a few cycles of flame pinch-off followed by global flame blowoff when ϕ falls below the lean flammability limit and (ii) flame pinch-off and flame-wall quenching together cause global flame blowoff.