Vapor-liquid equilibrium data at 35 kPa have been determined for the ternary system 1,1,1,2,3,4,4,5,5,5-decafluoropentane (HFC-4310mee) + 2-methylfuran + oxolane, and for their constituent binaries HFC-4310mee + 2-methylfuran and 2-methylfuran + oxolane, in the temperature range 297 to 310 K. Vapor pressures of 2-methylfuran have also been measured in the range of boiling temperatures of the mixture. Depending on the concentration range, the ternary system exhibits positive to negative deviations from ideal behavior and no ternary azeotrope has been detected. The binary system HFC-4310mee (1) + 2-methylfuran (2) exhibits positive deviations form ideal behavior and a minimum temperature azeotrope at a composition rich in HFC-4310mee (x(1) congruent to 0.561, T congruent to 297.55 K). The binary system 2-methylfuran (2) + oxolane (3) exhibits negative deviations form ideal behavior and a maximum temperature azeotrope at a composition rich in oxolane (x(2) congruent to 0.310, T congruent to 309.95 K). The vapor-liquid equilibrium data of the binary mixtures were correlated with the Redlich-Mster model and were used to predict the equilibrium properties of the ternary mixture. In addition, a model-free approach that is applicable to ternary mixtures has been used to analyze the properties of the ternary mixture.