Several stable oligo-mode spectra of a CW dye laser were recorded with the aid of an optical spectrum analyzer (scannable Fabry-Perot) giving Fourier transforms of the light field. Simultaneously the total intensity was measured with a fast photodiode and analyzed for beat signals with an RF spectrum analyzer. The spectra observed can be explained consistently in terms of a kinematic model postulating that competing modes cannot exist simultaneously and therefore show a "spiking" behavior. The repetition frequency of the spiking was found to be the frequency difference of the competing modes, a mechanism known from mode-locking. For the spectra observed experimentally, analytic expressions for the time development of the field amplitudes are given which are in good agreement with the experimental results.