We report measurements of the viscosity and density of two binary mixtures comprising hexadecane with dissolved carbon dioxide or methane over the temperature range from (298.15 to 473.15) K and at pressures up to 120 MPa. The measurements were conducted at various mole fractions x of the light component as follows: x = (0, 0.0690, 0.5877, and 0.7270) for xCO2 + (1 – x)C16H34 and x = (0, 0.1013, 0.2021, 0.2976, and 0.3979) for xCH4 + (1 – x)C16H34. The viscosity and density measurements were carried out simultaneously using a bespoke vibrating-wire apparatus with a suspended sinker. With respect to the first mixture, the apparatus was operated in a relative mode and was calibrated in octane whereas, for the second mixture, the apparatus was operated in an absolute mode. To facilitate this mode of operation, the diameter of the centerless-ground tungsten wire was measured with a laser micrometer, and the mass and volume of the sinker were measured independently by hydrostatic weighing. In either mode of operation, the expanded relative uncertainties at 95% confidence were 2% for viscosity and 0.3% for density. The results were correlated using simple relations that express both density and viscosity as functions of temperature and pressure. For both pure hexadecane and each individual mixture, the results have been correlated using the modified Tait equation for density, and the Tait–Andrade equation for viscosity; both correlations described our data almost to within their estimated uncertainties. In an attempt to model the viscosity of the binary mixtures as a function of temperature, density, and composition, we have applied the extended-hard-sphere model using several mixing rules for the characteristic molar core volume. The most favorable mixing rule was found to be one based on a mole-fraction-weighted sum of the pure component molar core volumes raised to a power γ which was treated as an adjustable parameter. In this case, deviations of the experimental viscosities from the model were within ±25%.