The invention relates to carbon nanotubes comprising hydroxy groups, wherein the surface thereof comprises hydroxy alkyl ester groups covalently bound thereon, chosen from the group according to the general formula (1) and/or the general formula (2), wherein (CNT) stands for the surface of the carbon nanotube and R1 and R2 are independently from each other hydrocarbon, an alkyl radical or an aryl radical. The invention further relates to a method for the production thereof by means of reaction of carbon acid groups of the carbon nanotubes with an epoxy, furthermore a polyurethane polymer, wherein said carbon nanotubes are covalently bound, a method for producing a polymer of said kind and use of the carbon nanotubes for producing polymers.