This paper presents new measurements of the viscosity of gaseous R404A (52 wt% R143a, 44 wt% R125, 4 wt% R134a), R407C (23 wt% R32, 25 wt% R125, 52 wt% R143a), R410A (50 wt% R32, 50 wt% R125), and R507 (50 wt% R143a, 50 wt% R125). These mixtures are recommended as substitutes for the refrigerants R22, R502, and R13B1. Measurements were carried out in an oscillating-disk viscometer. The obtained values of the viscosity are relative to the viscosity of nitrogen. The experiments were performed at atmospheric pressure over the temperature range 297 to 403 K. and near the saturation line up to pressures of 0.6 Pcrit. The estimated uncertainty of the reported viscosities are ±0.5% for the viscosities at atmospheric pressure and ± 1% along the saturation line, being limited by the accuracy of the available vapor pressure and density data. The experimental viscosities at atmospheric pressure are employed to determine the intermolecular potential parameters, σ and ɛ, which provide the optimum representation of the data with the aid of the extended law of corresponding states developed by Kestin et al. A comparison of the experimental viscosity data with the values calculated by REFPROP, both at atmospheric pressure and along the saturation line, is presented.