In this article, we report the structural and electronic properties of the double nanoring using the Density Functional Theory (DFT) formalism. The double nanorings were built with atoms of Boron (B), Aluminium (Al), Gallium (Ga), Indium (In), Thallium (Tl), Nitrogen (N), Phosphorus (P), Arsenic (As) or Bismuth (Bi). We calculated 19 new structures, being that these molecules showed stability for good convergence criteria. All calculated vibrational frequencies are positive for any molecule studied, indicating that all these structures are in a stable state. The calculated HOMO-LUMO gaps (HLgap) converged to values between 0.244 eV and 2.064 eV, showing promising electronic properties, except for the B8N8 nanoring that reached a HLgap of 4.739 eV, qualifying it as an insulating. The optical absorptions were also obtained for the double nanorings using the Time-Dependent Density Functional Theory (TD-DFT), and their dependence on the wavelength were analyzed, where four of these molecules absorb on the visible region (Al8N8, Al8P8, B8P8, Ga8N8 and Ga8P8).