The present invention pertains to polymer fibers obtainable by melt spinning at least one polymer and/or by processing at least one polymer in non-woven melt processes. The polymer fibers in accordance with the present invention exhibit a substantial free swell absorbency, rendering them suitable for use in inter alia absorbent products, for instance wound dressings. Additionally, the present invention relates to processes for obtaining said polymer fibers, absorbent articles comprising said fibers, as well as uses of said polymer fibers in products for treating wounds and/or bums.