The frequency behaviour of axial modes was investigated during the initial phase of mode competition in case of a helical TEA-CO2 laser. With the help of a homodyne technique single-shot and multi-shot beat spectra were measured. Analysing these under various aspects and combining the results of an earlier investigation it was found that a) inferior modes exist only for 100–200 ns. b) their spectral width is less than 1 MHz and is determined by lifetime broadening, with the dominant mode narrower than 0.77 MHz, c) in the average over many shots the spectral envelope of modes does not follow a Lorentzian shape as expected for the Lorentzian gain curve, d) the beat powers change widely from shot to shot, whereas the total laser power remains constant, e) no specific phase structures are likely to govern the laser emission, although the maximum emission principle appears to be obeyed with every individual shot. In an appendix relations are derived and summarized which are required for the evaluation of beat mode spectra and for the determination of line width as they apply to the actual time dependence of the laser emission.