In annular combustion chambers of aero-engines and gas turbines, acoustic coupling may arise from azimuthal modes which are less well damped than axial modes. Also, since the circumference is the largest length in the combustor, the azimuthal modes have the lowest resonance frequencies and are most prone to instability. Such a coupling raises many scientific issues which are considered in a small number of funda- mental experiments. The present investigation focuses on this problem and provides experimental data on a special type of combustion instability in which the thermo-acoustic resonant coupling involves a combina- tion of modes. This produces an unusual pattern of flame responses in which the distribution of heat release rate is slanted. Data are provided in the form of free radical light intensity patterns (interpreted as heat release rate distributions) and microphone signals detected in the plenum and chamber. It is shown that the slanted pattern is the signature of a combination of two modes with coinciding frequencies, the first being a standing azimuthal mode while the second is an axial mode. Measurements of the flame describing function on a single matrix burner at the fundamental frequency are used to explain the observed phase shift and amplitude in the flame responses of the different injectors in the annular combustor.