Results of measurements of solubility of eicosane in ethane and ethylene are presented. Measurements were performed in wide temperature and pressure intervals using a flow method. Investigations of the system ethane+eicosane were performed in the vapour–liquid equilibrium region. The system ethylene+eicosane was investigated both in the vapour–liquid equilibrium and solid–fluid equilibrium regions. The results obtained for this system show that the crystalline structure of solid eicosane has significant influence on its concentration in the gas phase. On the basis of the results obtained, influence of the proximity of the critical end point on the solubility enhancement is discussed. Results of calculations for the investigated systems with equation of state models are presented and discussed.