We analytically present the dispersion equation of an asymmetric three-layered chirowaveguides, in which the core and the claddings are different chiral materials. Then, we produce the dispersion equation for a symmetric three-layered chirowaveguides, in which the claddings chiral materials are the same, but different from the one in the core. After that, two modes of propagation through a chiral nihility core and left handed material (LHM) claddings waveguide are treated in details. The characteristic equations and the cut-off frequencies for both even and odd modes are derived. The electric field profiles are plotted and discussed. We show that each mode (odd and even) can be separated into right-handed and left-handed circularly polarized (RCP and LCP) modes. The results reveal that novel properties such as peculiar dispersion curves
