In this paper, we perform analytical and numerical studies of TEM-wave propagation in a coaxial waveguide filled with a graded periodic RHM-LHM composite, for which the real parts of the effective permittivity and permeability vary along the propagation direction (chosen to be the z-direction) according to an arbitrary periodic function. We obtain an excellent agreement between analytical and numerical results in the important special case of abrupt transitions between the two materials.