A resonator system for generating a radio frequency (RF) magnetic field in a volume under investigation of a magnetic resonance (MR) arrangement, comprises a number N of individual resonators (2) which surround the volume under investigation and which are each disposed on a flat dielectric substrate (1) around a z-axis, wherein the individual resonators (2) have windows (8) through each of which one individual RF field is generated in the volume under investigation in single operation of the individual resonators (2) and, through cooperation among the individual resonators (2), a useful RF field (7) is generated in the volume under investigation, wherein a remote RF field (6) is asymptotically generated far outside of the resonator system, and the spatial distribution of the useful RF field (7) is substantially mirror-symmetrical relative to a first plane A which contains the z-axis, and that of the asymptotic remote RF field (6) is substantially mirror-symmetrical relative to a second plane B which contains the z-axis, the useful RF field (7) extending substantially parallel to the first plane A in the volume under investigation, wherein the number of individual resonators (2) is N>4 and wherein, during operation of the resonator system at at least one point in time, the substrate plane of at least one individual resonator (2) subtends an angle of more than 40.degree. with respect to the direction of the useful RF field (7) in the volume under investigation, and at least one further individual resonator (2) subtends an angle of less than 40.degree. with respect to the direction of the useful RF field (7) in the volume under investigation, is characterized in that the first plane A is not rotated about the z-axis relative to the second plane B or is rotated by less than 360.degree./(N+1). The inventive resonator system realizes a resonator system with improved field homogeneity and full quadrature suitability, high quality factor and large efficiency using straightforward constructional measures.