A coaxial phase shifter for very high RF-powers includes an optionally-cooled housing which forms the outer conductor and in which a substantially U-shaped inner conductor made of a tube is arranged which comprises at each of its ends a cooling medium connection for guiding through a cooling medium. The U-shaped inner conductor is externally displaceable for changing its electrical length between a contact-making input-side inner-conductor connection piece and a contact-making output-side inner-conductor connection piece. The inner-conductor connection pieces are disposed coaxially in the outer connection flanges which make contact with the housing.