We present viscosity measurements of three (methane + ethane) gas mixtures as well as of the pure fluids methane and ethane over the temperature range from (253.15 to 473.15) K at pressures between (0.1 and 2.0) MPa; the relative expanded combined uncertainty (k = 2) in viscosity ranges between (0.16 and 0.49) %. Measurements were carried out relative to helium using a rotating-body viscometer. The composition of the commercially purchased gas mixtures was verified in-house through highly accurate density measurements utilizing a well-proven two-sinker magnetic-suspension densimeter. We compare our experimental viscosities to experimental literature data, recent ab initio calculated values and correlations. Around ambient conditions, the new pure fluid data do not differ more than 0.1 % from reference and ab initio calculated values. At the highest temperature of the present study, deviations of the new data to ab initio data increase to 0.20 % and 0.33 % for methane and ethane, respectively. For an appropriate evaluation of the binary mixture data and for the purpose of data comparison, a second-order viscosity virial correlation for the present mixture was fitted to the experimental data for the pure fluids and for one mixture. The correlation is based on the modified Enskog theory for hard sphere mixtures. As a result, the relative deviations of the pure fluid data do not exceed 0.15 %, and the maximum relative deviation of all viscosity data from the model was 0.22 %. This implies that all experimental viscosity data are reproduced or predicted, respectively, within their experimental uncertainties.