Thermodynamic analysis of air separation units (ASUs) for obtaining gaseous oxygen under pressure has been conducted. We compared parameters of ASUs working on a production scheme with the produced oxygen compressed in the compressor and liquid oxygen compressed in the pump with subsequent heating to ambient temperature. In the result of the research, a dimensionless criterion has been derived, the physical meaning of which is that it is the ratio of the work done in the oxygen compressor to the additional work that must be done to compensate for thermodynamic losses associated with the operation of the pump of liquid oxygen. An example of the use of these relations for the analysis of ASU running on the medium pressure cycle and designed to produce gaseous oxygen at a pressure of 16 MPa is considered. From the thermodynamic analysis of such unit, it follows that energy consumption for oxygen compression in the scheme with the pump can be approximately 1.5 times less than the energy consumption when oxygen compressor is used. Analysis of low pressure ASU has shown that at the pressure of the produced oxygen below 7.8 MPa, schemes with the liquid oxygen pump are more efficient than conventional schemes with the compression of produced oxygen. When the pressure of the produced oxygen is above 8.7 MPa, the scheme with an oxygen compressor becomes more energy efficient.