The invention describes novel polymer-functionalized carbon nanotubes. These comprise a carbon nanotube, a first polymer that is adsorbed on the outer surface of a carbon nanotube and comprises amino groups, and a second polymer covalently bonded to the first polymer. The bond between the second polymer and the first polymer is formed by the reaction of amino groups from the first polymer with groups from the second polymer that are reactive with respect to amino groups. The invention further relates to a method for the production thereof, wherein carbon nanotubes are provided in an aqueous solution of a first polymer comprising amino groups and then a solution of a second polymer comprising groups that are reactive with respect to amino groups is added. The invention also relates to the use of the carbon nanotubes in dispersions, polymers and surface coatings.