In this study, the liquefaction system of various components in the air was investigated by cryogenic method. Advanced exergy analysis was applied to the cryogenic liquefaction system. The study focused on the liquefaction system integrated into the air separation unit (ASU). Three different working fluids were selected i.e. nitrogen, oxygen and argon. In traditional exergy analysis, while calculating exergy efficiency and exergy destruction rates for all three fluids, endogenous, exogenous, avoidable and unavoidable exergy destruction values were also calculated with advanced exergy analysis. As a result of this study, exergy efficiency of argon, nitrogen and oxygen elements were found to be 51.77%, 56.13% and 53.35%, respectively. Therefore, it was calculated that the endogenous exergy destruction, which was one of the advanced exergy components for the whole system and working fluids, was approximately 80-95%.