The densities of three ternary mixtures of methane, n-butane and n-hexadecane and three quaternary mixtures of methane, n-butane, n-heptane and n-hexadecane were measured. The ternary mixtures were studied over the temperature range 295-350 K and the pressure range 8.3-49.3 MPa at the following methane mole fractions: 0.0185, 0.0358 and 0.0478 and corresponding n-butane mole fractions: 0.8680, 0.8527 and 0.8422. The quaternary mixtures were studied over the temperature range 317-460 K and the pressure range 26.9-49.7 MPa at the following methane mole fractions: 0.1210, 0.1717 and 0.2186 and corresponding n-butane mole fractions: 0.1632, 0.1537 and 0.1450 and n-heptane mole fractions: 0.5791, 0.5457 and 0.5148. The measurements were carried out in an automated isochoric instrument and their accuracy is estimated to be better than +/-0.1%. The bubble points of the quaternary mixtures were determined from an analysis of the experimental isochores in the one- and two-phase regions. The new measurements have been used to assess the performance of the Peng-Robinson equation of state and the one-fluid corresponding states model. In single phase regions, the performance of the one-fluid model is found to be superior to that of the Peng-Robinson equation.