Previous work [Biagioli, F., Stabilization mechanism of turbulent premixed flames in strongly swirled flows, Combustion, Theory and Modelling 10 (3) (2006) 389–412; Guethe, F., Lachner, R., Schuermans, B., Biagioli, F., Geng, W., Inauen, A., Schenker, S., Bombach, R., Hubschmid, W., Flame imaging on the ALSTOM EV-burner: thermo acoustic pulsations and CFD-validation, in: AIAA Paper 2006-437 presented at the 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, January 9–12, 2006] has shown that turbulent dry low NO x (partially premixed) flames in high swirl conical burners may be subject to a large change of their anchoring location at the symmetry axis when a critical value of the bulk equivalence ratio is reached, i.e. they are bi-stable. This flame behavior is linked here to combustion pressure dynamics measured in an atmospheric test rig for a prototype version of the Alstom EnVironmental (EV) conical burner. The link is made via the solution of the problem of the ‘travelling flameholder’, which shows that the unsteady displacement of the flame anchoring location implies an unsteady variation of the flame surface area and therefore unsteady heat release. The relevance of this source of unsteady heat release—which is different from more usual ones due to variations in turbulent burning rate and in the sensible enthalpy jump across the flame—to the generation of combustion dynamics in strongly swirled flows is confirmed here by the strong positive correlation between the tendency of the flame to be displaced and the measured amplitude of pressure pulsations.