On the basis of known methods, installations and systems for cooling the carrier fuel components: oxygen and liquefied methane, a schematic diagram of a nitrogen system built on the basis of turbo-expander nitrogen liquefiers for cooling liquefied methane when refueling a medium-class carrier rocket has been developed. With the use of specialized software for modeling chemical processes (Aspen Hysys (v. 8.4)), mathematical modeling of schemes for competing variants and their elements was performed. The competing options are: – the scheme of a medium-capacity nitrogen liquefier with a nitrogen screw compressor and a low-pressure nitrogen turbo expander with an oil brake (scheme A); – the scheme of a medium-capacity nitrogen liquefier with a low-pressure nitrogen turbo expander with a booster compressor unit (scheme B). The comparison of competing variants for the basic technological scheme of the nitrogen cooling system for liquefied methane by the indicator-coefficient of nitrogen liquefaction (c) was made. The results of the work can be used in the design of nitrogen systems of liquefied methane cooling for refueling medium-class launch vehicles with under-heated high-density methane.