The physical peculiarities of the wave propagation in coupled cylindrical slot lines are studied in the context of a rigorous electromagnetic theory. The mode analysis is performed. The approximate dispersion equations of the lowest waves in symmetrically coupled cylindrical slot lines are derived and the splitting of the wave spectrum is considered. The numerical analysis of the rigorous dispersion equation yields the wave dispersion characteristics depending on geometrical and constitutive parameters. The calculation results of the field structure of the modes are presented. A New peculiarity of the phenomenon of the waves mutual transformation is discussed.