A web of a polymer film (1) is coated with an oxide layer, in particular with an SiOx barrier layer, by transporting the web with the aid of a rotatable drum (12) through a plurality of flame bands, which are directed in a radial direction from above against the circumferential surface of the drum, which extend at a distance from each other across the width of the web being supported and transported on this circumferential surface, and which are fed with a gas mixture including a combustible gas, an oxidant, and a silicon containing compound. Therein the circumferential surface of the rotatable drum is cooled to a predetermined temperature and the web is transported through the area of the tip of the inner flame region. Polymer films with barrier layers produced in the named way have at small layer thicknesses of less than 10 nm very good barrier properties.