An apparatus combining a vibrating-wire viscometer and a single-sinker densimeter was used to provide accurate eta ppT data for four isotherms on ethane at (293.15, 307.15 [ethane 3.5 and 5.0], and 423.15) K and five isotherms on propane at (273.15, 298.15, 366.15, 373.15, and 423.15) K. The maximum pressure was chosen to be about 95 % of the saturated vapor pressure for the subcritical isotherms and 30 MPa at maximum for the supercritical isotherms. The relative uncertainty in the density is estimated to be less than +/- 0.1 %, except for the low-density range. Near the critical region, allocation errors for temperature and pressure have a significant impact on the uncertainty of the experimental densities. The density data agree within +/- 0.1 %, when comparing them with values calculated from the equations of state by Bucker and Wagner (2006) for ethane and by Lemmon et al. (2009) for propane, excluding the low-density and the near-critical regions. The near-critical isotherms at 307.15 K for ethane and at 373.15 K for propane reveal differences of +2.1 % and +1.2. %, respectively, in accordance with the estimated maximum total uncertainties of the experimental eta ppT data for these isotherms. The viscosity measurements are characterized by a relative uncertainty of +/- (0.25 to 0.3) %, only increased by 0.04 % in the near-critical region due to the allocation errors arising from the temperature and density measurements. The new viscosity data and additionally re-evaluated earlier data of our group are compared with the viscosity surface correlations by Hendl et al. (1994) for ethane and by Scalabrin et al. (2006) for propane as well as with selected experimental data for the low-density region. For ethane, the maximum deviations of the new data exceed the stated uncertainty of +/- 2.5 % for the viscosity surface correlation. For propane, the deviations do not exceed +/- 0.7 %, except for the nearcritical isotherm at 373.15 K The effect of the critical enhancement became evident for the near-critical isotherms, about 2 % for ethane at 307.15 K and about 1 % for propane at 373.15 K. The new viscosity data should be used to improve the viscosity surface correlations available in the literature.