The invention provides a biocompatible filament material having an antimicrobial finish, in particular in the form of a surficial layer, the finish comprising polyhexamethylenebiguanide (PHMB) as a nonspecifically antimicrobially active component, and also a process for producing the filament material, comprising the steps of: producing an active solution from the nonspecifically antimicrobially active component PHMB and a solvent, transferring PHMB from the active solution onto and/or into the filament material, and drying the filament material comprising the transferred PHMB.