The present disclosure relates to systems and methods useful for power production. In particular, a power production cycle utilizing CO.sub.2 as a working fluid may be combined with a second cycle wherein a compressed CO.sub.2 stream from the power production cycle can be heated and expanded to produce additional power and to provide additional heating to the power production cycle.

A process for cryogenic fractionation of air uses an air fractionation plant (100-400) comprises a rectification column system (10) having a high-pressure column (11) operated at a pressure level of 9 to 14.5 bar, a low-pressure column (12) operated at a pressure level of 2 to 5 bar, and an argon column (13). A recirculating stream is formed using a second top gas or a portion thereof, which is heated, compressed, cooled again, and after partial or complete liquefaction or in the unliquefied state is introduced partially or completely, or in fractions, into the first rectification column (11) and/or into the second rectification column (12).