Critical loci of 1-hexene/CO2 and (hexene isomer pseudo-component)/CO2 binary mixtures, along with the critical properties of the ternary mixture of CO2/1-hexene/(hexene isomer pseudo-component) were predicted using Gibbs’ thermodynamic criteria for criticality in conjunction with the Peng-Robinson (P-R) EOS. Maximum deviation in the critical pressures of the 1-hexene/CO2 binary mixture is less than 2% from reported experimental values. The addition of hexene isomer to the 1-hexene/CO2 binary and the path of approach to mixture critical points are shown to have surprisingly strong effects on predicted mixture critical properties. For a given ternary mixture, multiple critical points are predicted depending upon the isopleth (either constant CO2 mole fraction path or constant 1-hexene mole fraction path) along which the critical point is approached. Critical densities predicted along the CO2 isopleth of approach to critical points are always smaller than the ones predicted along the 1-hexene isopleth of approach. Furthermore, upon hexene isomer addition to the 1-hexene/CO2 binary, whereas the predicted critical property surfaces of the ternary system vary monotonically along the CO2 isopleth of approach, extrema in these surfaces are predicted when approaching the mixture critical points along 1-hexene isopleths. These anomalous predictions are attributed to the inability of the cubic EOS to accurately model the phase behavior near the critical point.