In this paper, we propose, design and test a new dual-nuclei RF-coil inspired by wire metamaterial structures. The coil operates as a result of resonant excitation of hybridized eigenmodes in multimode flat periodic structures comprising several coupled thin metal strips. It was shown that the field distribution of the coil (i.e. penetration depth) can be controlled independently at two different Larmor frequencies by selecting a proper eigenmode in each of two mutually orthogonal periodic structures. The proposed coil requires no lumped capacitors to be tuned and matched. In order to demonstrate the performance of the new design, an experimental preclinical coil for 19F/1H imaging of small animals at 7.05T was engineered and tested on a homogeneous liquid phantom and in-vivo. The results demonstrate that the coil was both well tuned and matched at two Larmor frequencies and allowed image acquisition at both nuclei. In an in-vivo experiment, it was shown that without retuning the setup it was subsequently possible to obtain anatomical 1H images of a mouse under anesthesia with 19F images of a tiny tube filled with a fluorine-containing liquid and attached to the body of the mouse.