An analysis of electromagnetic wave propagation in mutually coupled parallel lines is carried out. The theory is then adapted to microwave propagation in waveguides capable of supporting simultaneously a large number of modes, and explicit solutions are obtained in the case of weak coupling.A detailed analysis of periodically coupled modes is developed and applied to a number of specific cases of practical interest. It is shown that, although very weakly coupled waveguides have negligible influence on signal distortion, periodic coupling results in considerable signal distortion. A waveguide with random irregularities is treated in some detail and explicit formulae for signal distortion are derived.The analysis is concluded with numerical examples illustrating signal distortion, increase in attenuation and echo distortion.