Coupled oscillations of ring lattices with different types of dielectric resonators are considered. New analytical equations for complex frequencies and amplitudes of resonators, without restrictions on their number, are obtained. General analytical solutions for the frequencies and amplitudes of coupled oscillations for different ring lattices built on different resonators are found. It is noted that the obtained equations are also suitable for describing coupled oscillations of a ring lattices with degenerate oscillations of resonators, as well as with structures that contain ring lattices with different number elements. In general, the solutions for eigen waves propagating in periodic ring structures of DR are found. The solutions for several ring lattices consisting of two, three and four resonators of different types are compared with the numerical values found from the eigenvalues of the general coupling matrix. Good agreement between the analytical and the numerical results of calculating of the coupling matrix eigenvalues is demonstrated. The developed theory is the basis for the design and optimization of parameters of different devices of the microwave, theraherz and optical wavelength ranges, that built on a large number of dielectric resonators of various types. New equations obtained for calculating coupled oscillations of dielectric resonators also allow build more efficient models of scattering for optimization of various dielectric metamaterials.