A general mathematical treatment of vibronic coupling of two electronic states in molecules and dimers is presented. The 2times;2 matrix Hamiltonian which is derived is shown to reduce to two onehyphen;dimensional Hamiltonians provided a certain minimum amount of symmetry is present. Some general selection rules governing electronic transitions to these states from the ground state are obtained, showing that the spectral distribution in hot bands may differ considerably from that in normal bands when vibronic coupling occurs. A special model which considers the coupling to arise from a single mode of vibration is presented. Two limiting cases which can be treated approximately by perturbation theory are considered in detail. These are shown to give rise to a ``pseudo Jahnhyphen;Teller effect'' and to vibrational borrowing in the two different limits.
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