Abstract: Single or double column cryogenic gas-separation/liquefaction devices, where refrigeration to the device is supplied by a cryocooler alone or by a combination of a cryocooler and by a Joule-Thompson throttling process, where the gas condensation may occur directly on the cold portion of the cryocooler which may be located inside of the thermally insulated space of the distillation column(s) are disclosed. The system is particularly useful for medical applications, such as providing for safe and economical high-purity oxygen for at-home use. The invention principles include a combined column embodiment for simultaneous production of high-purity liquid or gaseous oxygen and nitrogen. Another double column design offers reduced temperature and pressure separation with easy switching between oxygen and nitrogen extraction or single component extraction. If both gaseous and liquid oxygen are required, oxygen purity of approximately 95% can be produced with good recovery, i.e.