The frequency response of premixed swirled flames is investigated by comparing their Transfer Function (FTF) between velocity and heat release rate fluctuations. The equivalence ratio and flow velocity are kept constant and four different swirling in-jectors are tested with increasing swirl numbers. The first injec-tor features a vanishing low swirl number S = 0.20 and produces a flame anchored by the recirculating flow in the wake of a central bluff body. The three other swirling injectors produce highly swirled flows (S > 0.6) leading to a much larger internal recir-culation region, which size increases with the swirl level. When operating the burner at S = 0.20, the FTF gain curve smoothly increases to reach a maximum and then smoothly decreases towards zero. For the highly swirled flames (S > 0.6), the FTF gain curve shows a succession of valleys and peaks attributed to interferences between axial and azimuthal velocity fluctuations at the injector outlet. The FTF phase-lag curves from the vanishing low and highly swirled flames are the same at low frequencies despite their large differences in flame length and flame aspect ratio. Deviations between the FTF phase lag curves of the different swirled flames start above the frequency corresponding to the first valley in the FTF gain of the highly swirled flames. Phase averaged images of the axial flow fields and of the flame chemiluminescence are used to interpret these features. At forcing frequencies corresponding to peak FTF gain values, the cold flow response of all flames investigated is dominated by large coherent vortical structures shed from the injector lip. At forcing frequencies corresponding to a valley in the FTF gain curve of the highly swirled flames, the formation of large coherent structures is strongly hindered in the cold flow response. These observations contrast with previous interpretations of the mechanisms associated to the low FTF response of swirled flames. It is finally found that for flames stabilized with a large swirl number, heat release rate fluctuations result both from large flame luminosity oscillations and large flame volume oscillations. For conditions leading to a small FTF gain value, both the flame luminosity and flame volume fluctuations are suppressed confirming the absence of strong perturbations within the flow at these frequencies. The experiments made in this work reveal a purely hydrodynamic mechanism at the origin of the low response of swirling flames at certain specific frequencies.