A method for surface treatment of a fibrous polyphenylene sulfide or polysulfone is based on the use of a gas mixture of 1 to 5% in volume of elemental fluorine, of nitrogen as carrier gas and of no more than 20% in volume elemental oxygen. The gas mixture affects the fibers until the total fluorine content in the fiber material is between 0.01 and 0.2 percent in weight. The fibers treated in this manner are particularly suited as separator material in electrochemical energy storage devices with an alkaline electrolyte.