The viscosities of a series of water-bearing peralkaline rhyolitic melts have been experimentally determined. The dry melt compositions are composed of a series of additions of Na₂O to a metaluminous base composition. The melts, initially hydrated at high pressures and quenched isobarically, have been prepared by cutting and polishing, then reheating across the glass transition at 1 atm where they are annealed to a relaxed metastable state and then investigated dilatometrically using micropenetration methods. The measurements have been performed in the viscosity range of 10^8.5–10^11.5 Pa s which corresponds to temperatures in the range of 675–220°C for these compositions. Despite the relatively low viscosities of dry peralkaline melts in comparison with metaluminous melts of similar SiO₂ content, the viscosities of peralkaline rhyolitic melts also decrease strongly and non-linearly with the addition of water. The resulting viscosity–temperature relationships for water-bearing peralkaline rhyolitic melts are shifted to much lower temperatures such that glass transition temperatures for moderate cooling rates correspond to extraordinarily low temperatures. A model is presented for the calculation of melt viscosities in the range of 10^8.5–10^11.5 Pa s for peralkaline rhyolites with up to 7 wt% H₂O. The very fluid nature of these peralkaline rhyolites over a wide range of water contents may facilitate a very efficient degassing history of glassy peralkaline rhyolites in nature. Efficient degassing might explain the apparent contradiction of the presence of common water-rich melt inclusions in phenocryst phases hosted in water-free glassy rhyolites, versus the absence of vesicular layers or textural evidence for a vesicular past for the glassy rocks.