In this paper a system of transmission lines coupled by reactive networks at regular intervals is examined. If the coupling networks are identical, it is shown that modes of propagation, equal in number to the number of lines, can exist. These modes are typified by voltage and current distributions which can be determined from the properties of the network, and show similarities to waveguide modes. In particular, the modes are orthogonal in that the power flow when several modes exist is given by the contributions of the modes considered one at a time.