An antenna structure for exciting a substantially homogeneous magnetic RF field and/or for receiving RF signals in a nuclear magnetic resonance tomography apparatus includes a hollow cylindrical conductor sheath which is substantially transmissive at low frequencies for gradient magnetic fields, a number of conductor units within the conductor sheath, each conductor unit including at least one conductor element, and RF reflector disposed at the end faces of the antenna structure and an external energy feed or reception device. In this antenna structure, the current drop which increasingly occurs toward the end faces of the antenna structure is largely compensatable by shaping the electrically conductive cross-section of the conductor units so as to decrease symmetrically from an axial center of the antenna structure moving toward the end faces of the structure. The conductor units thus have a largest cross-section at a center of the antenna structure, and a smallest cross-section at the end faces.