Abstract: By employing the method of the separation of variables in the circular-cylindrical system, a recursive formula for the electromagnetic fields in the metal coaxial line filled with multi-layer reciprocal chiral media is derived. The general mode eigenequation is given. In the same way the eigenequation for the metal circular waveguide filled with multi-layer reciprocal chiral media can also be obtained. From the general eigenequations of the metal coaxial line and the metal circular waveguide filled with multi-layer reciprocal chiral media, the mode eigenequations of the coaxial line and the circular waveguide filled with one-layer reciprocal chiral medium can be obtained. When the chiral parameter equals zero, the mode eigenequation of the metal coaxial line filled with ordinary one-layer