The invention relates to a method and an arrangement for the continuous production of compressed oxygen from air using mixed conducting ceramic membranes. The aim of the invention is to provide a way of isolating pure oxygen from the air and compressing said oxygen to pressures above the ambient pressure, without using mechanical or electromechanical compression of air or oxygen. To achieve this aim, according to the invention water in various aggregate states is conducted in a circuit and the configuration of the equipment is designed such that the desired high oxygen pressure is produced in a separate area from the membrane module and the oxygen produced is prevented from mixing with the freshly produced water vapour.