The role of phases in local Communication Theory of the Chemical Bond is investigated. Probability amplitudes of such molecular ( fine -grained) information systems originate from the superposition principle of quantum mechanics involving the projection onto the bond system defined by the subspace of the state occupied Molecular Orbitals. They are explicitly phase -dependent, thus being capable of inter- ference effects. The phase factors of the local direct and indirect (bridge, cascade) channels are examined and the associated amplitude/probability sum rules are estab- lished. The entropic descriptors of the local channels, providing the system “covalent” (communication- noise ) and “ionic” (information- flow ) components, are investigated using prototype one -electron systems. The competition between these information- theoretic measures of the chemical bond covalency (electron delocalization) and ion- icity (electron localization) is illustrated in H + 2 and H 2.