The invention relates to a radio-frequent (RF) coil system (17, 17') for use in a magnetic resonance imaging (MRI) system. The RF coil system comprises at least one main coil (35) for transmitting an RF magnetic field (B.sub.1) into and/or receiving an RF magnetic field (B.sub.1') from an examination volume (3) of the MRI system. The main coil has a main coil axis (37), which is or is to be oriented parallel to a main magnetic field (B.sub.0) in the examination volume, and at least one electrical conductor (39, 41) which extends mainly parallel to the main coil axis. According to the invention, the RF coil system comprises at least two electrical auxiliary coils (51, 53, 55, 57) which are assigned to said conductor of the main coil. The auxiliary coils are arranged on opposite sides of said conductor of the main coil. Each auxiliary coil has a coil axis (59, 61, 63, 65) which extends substantially parallel to the main coil axis at a distance from the conductor of the main coil to which the respective auxiliary coil is assigned, said distance being small relative to a main dimension (L) of the main coil. The auxiliary coils constitute passive electrical coils in which electrical currents are generated under the influence of an RF magnetic field (B.sub.11, B.sub.11') present at the location of the auxiliary coils. The RF magnetic field (B.sub.12, B.sub.34) generated by the auxiliary coils as a result of said currents in the auxiliary coils suppresses said RF magnetic field present at the location of the auxiliary coils. Thus, the auxiliary coils provide a sensitivity reducing effect of the RF coil system in local regions (47, 49) which are at relatively small distances from the conductor of the main coil. For regions at a distance from the conductor of the main coil comparable to the main dimension of the main coil, said sensitivity reducing effect is negligible.