Abstract: An axially stepped annular combustion chamber, especially of an aircraft gas turbine, has an essentially independent main combustion chamber 5' as well as an independent pilot burner chamber 5. An appropriate design of internal limiting walls 6a, 6b of pilot burner chamber 5 ensures that the combustion gases enter the main burner zone 5' essentially in the radial direction. This ensures optimum mixing of the fuel with air in this main combustion zone and/or main combustion chamber 5', thus minimizing exhaust emissions and ensuring optimum temperature distribution at combustion chamber outlet 8. Internal limiting wall 6a can have a deflecting section 12 or outer wall section 6b can run at an angle to pilot burner lengthwise axis 3a, so that the cross section of pilot burner zone 5 is reduced in the flow direction.