In order to acquire image or MR spectra at two different nuclei dual-frequency RF-coils are used. Conventional approaches of tuning and matching a coils at several frequencies employ expensive non-magnetic capacitors which also introduce dissipative losses. We propose an alternative method of tuning and matching the coils at multiple desired frequencies. This method is based on resonant excitation of hybridized eigenmodes of periodic structures of metal strips. The proposed method allows one to build cheap coil with reduced dissipative losses resonating on two different frequencies simultaneously.