System with a TEM resonator system especially for use in an MR imaging system and a gradient coil system (61, 62), wherein the gradient coil system (61, 62) coaxially surrounds at least a part of the TEM resonator system and comprises a recess or a gap, the system comprising: - a first TEM cylindrical volume resonator which comprises a first RF shield and a plurality of first conductors which are capacitively or galvanically coupled to the first RF shield, a second TEM cylindrical volume resonator which comprises a second RF shield and a plurality of second conductors which are capacitively or galvanically coupled to the second RF shield, and a third TEM cylindrical volume resonator which comprises a third RF shield and a plurality of third conductors which are capacitively or galvanically coupled to the third RF shield, wherein the first TEM cylindrical volume resonator, the second TEM cylindrical volume resonator and the third TEM cylindrical volume resonator are arranged and displaced from each other along a common longitudinal axis so that an intermediate section between each pair of adjacent TEM resonators is created, which is aligned with the respective longitudinal axis of each of the first TEM cylindrical volume resonator, the second cylindrical TEM volume resonator and the third TEM cylindrical volume resonator, - a first intermediate RF shield which is positioned between the first and the second TEM cylindrical volume resonator and which capacitively or galvanically connects the first RF shield with the second RF shield, and - a second intermediate RF shield which is positioned between the second and the third TEM cylindrical volume resonator, wherein - the first intermediate RF shield is composed of at least one radial ring (41r1, 41r2) and at least one cylindrical ring, both being arranged coaxially with the common longitudinal axis, wherein the inner and/or the outer radial dimension of the at least one radial ring and/or the axial length and/or the radial dimension of the at least one cylindrical ring being dimensioned for at least substantially preventing electromagnetic radiation from emanating outward from between the first TEM cylindrical volume resonator and the second TEM cylindrical volume resonator toward their surroundings, i.e. having a component propagating in the radial direction from the common longitudinal axis through the intermediate section into the surroundings, and wherein - the first and the second intermediate RF shield and the conductors (21, 22, 23) of the first to third TEM cylindrical volume resonator are positioned within the recess. - a first TEM cylindrical volume resonator which comprises a first RF shield and a plurality of first conductors which are capacitively or galvanically coupled to the first RF shield, a second TEM cylindrical volume resonator which comprises a second RF shield and a plurality of second conductors which are capacitively or galvanically coupled to the second RF shield, and a third TEM cylindrical volume resonator which comprises a third RF shield and a plurality of third conductors which are capacitively or galvanically coupled to the third RF shield, wherein the first TEM cylindrical volume resonator, the second TEM cylindrical volume resonator and the third TEM cylindrical volume resonator are arranged and displaced from each other along a common longitudinal axis so that an intermediate section between each pair of adjacent TEM resonators is created, which is aligned with the respective longitudinal axis of each of the first TEM cylindrical volume resonator, the second cylindrical TEM volume resonator and the third TEM cylindrical volume resonator, - a first intermediate RF shield which is positioned between the first and the second TEM cylindrical volume resonator and which capacitively or galvanically connects the first RF shield with the second RF shield, and - a second intermediate RF shield which is positioned between the second and the third TEM cylindrical volume resonator, wherein - the first intermediate RF shield is composed of at least one radial ring (41r1, 41r2) and at least one cylindrical ring, both being arranged coaxially with the common longitudinal axis, wherein the inner and/or the outer radial dimension of the at least one radial ring and/or the axial length and/or the radial dimension of the at least one cylindrical ring being dimensioned for at least substantially preventing electromagnetic radiation from emanating outward from between the first TEM cylindrical volume resonator and the second TEM cylindrical volume resonator toward their surroundings, i.e. having a component propagating in the radial direction from the common longitudinal axis through the intermediate section into the surroundings, and wherein - the first and the second intermediate RF shield and the conductors (21, 22, 23) of the first to third TEM cylindrical volume resonator are positioned within the recess.