This paper describes the working mechanism of binary cryogenic mixtures containing nitrogen and alkanes or alkenes. The Peng-Robinson equation of state is used to calculate the mixed free enthalpy of these mixtures and a method to calculate the mutual solubility is also suggested. Finally, the vapour-liquid, liquid-liquid and vapour-liquid-liquid equilibria of these mixtures are analysed. Therefore, an effective method to predict the characteristics of new kinds of binary cryogenic substances is provided in this paper.