In this study, as a result of the photometric observations continued on nine UV Ceti type stars, examining the parameters obtained from the models of distributions of the flare equivalent durations in the logarithmic scale versus flare total durations, it is found that the highest flare equivalent durations occurring on the stars (Plateau values) are varying with the B - V colour indexes of those stars in agreement with the variations of both the magnetic field strength (B) of the magnetic loop and especially the electron density of its plasma (n(e)). The distributions of flare cumulative frequencies were derived by using the flare equivalent durations, instead of the flare energy. The main result of this study is a secondary variation, which can be just modelled with the damping sine waves, behind the main exponential variation of the flare cumulative frequency. The models indicate that this secondary variation in the flare cumulative frequency distributions is in the same shape with the periodic or quasi-periodic oscillations detected in the light curves of the stellar and solar flares. This caused to ask new questions about the flare mechanism working on stellar atmospheres.