The viscosity of compressed liquid 1,1,1-trifluoroethane (HFC-143a) and pentafluoroethane (HFC-125) has been measured with a vibrating-wire viscometer at five temperatures between ( 254 and 293) K. The measurements were performed at pressures from above saturation up to 10 MPa, although for the isotherms at about 254 K the maximum pressure was approximately 5 MPa for HFC-143a and 7.4 MPa for HFC-125. For the isotherm at about 263 K, the highest pressure for HFC-143a was of the order of 7.5 MPa. The overall uncertainty of these results has been estimated to be less than +/- 1.0 %. The measurements have been correlated using a scheme based on a hard-spheres model. The root mean square deviation of the experimental results from the correlations for HFC-143a and HFC-125 is +/- 0.24 % and +/- 0.25 %, respectively. The correlation scheme has been used to perform the small extrapolations of the present data to the saturation line to enable comparison with literature results at saturation pressure.