The present invention relates to polymer compositions comprising at least one hydrophobic polymer and at least one modified polyisobutene; fibers, films, moldings and their further processing products formed from this polymer composition, a process for producing the polymer composition according to the present invention, a process for producing the fibers, films and moldings formed from the polymer composition according to the present invention; dyed polymer compositions comprising at least one hydrophobic polymer, at least one modified polyisobutene and at least one dye; and also fibers, films and moldings formed from the dyed polymer composition according to the present invention and the use of modified polyisobutenes for treating hydrophobic polymers.