A method for separating carbon dioxide from a flue gas using a membrane (membrane module) is characterized in that the flue gas is at temperatures above the condensation point of the water vapor before entering the membrane separation stage. In this way, condensation of any potentially entrained water vapor out of the flue gas is avoided, so as to consistently prevent clogging of the membrane pores. The high temperatures can be achieved in different ways. The temperature of the flue gas can easily be increased to the necessary temperatures by way of an upstream heat exchanger or a burner. A compressor, which is connected upstream of the membrane module and also advantageously increases the CO.sub.2 partial pressure, brings about the necessary temperature increase at the same time. As a further alternative for the invention, the CO.sub.2 separation is performed even before desulfurizing the flue gas. This notably has the advantage of the flue gas in this process stage still being at temperatures above the condensation point of the water vapor, and thus not having to be heated separately, in addition to which, it generally carries little water vapor at this stage of the scrubbing operation.