By using the method of separation of variables in the elliptical-cylindrical coordinate system,the mode eigenequation for a confocal elliptical coaxial line filled with multilayer dielectrics is presented. When the elliptical coaxial line becomes a circular coaxial line,the mode eigenequation of the circular coaxial line can be obtained from the mode eigenequation of the elliptical coaxial line using the asymptotic formulae of angular and radial Mathieu functions. The results show that the mode eigenequation of a circular coaxial line filled with multilayer dielectrics can be treated as a special case of an elliptical coaxial line. When the major semi-axis value of the interior conductor of an elliptical coaxial line equals zero,the elliptical coaxial line becomes an elliptical waveguide. In the same way,the mode eigenequation of the elliptical waveguide filled with multilayer dielectrics is derived. When the elliptical coaxial line or elliptical waveguide is only filled by one layer dielectric,the mode eigenequations for them are obtained from the general mode eigenequations. These results are consistent with other scientific literatures. Finally,numerical results for some modes are presented to analyze the propagation characteristics influenced by the dielectrics filled in the confocal elliptical coaxial lines and influenced by their structures,etc.