For the singlet-singlet annihilation process S-1+S-1-->S-2+S-0, an expression is derived for the electronic coupling matrix element involved in electronic excitation energy transfer (EET) between two equivalent chromophores. Allowance is made for vibronic coupling to occur between the S-1 and S-2 states of the chromophores, for each of which the S-1<-- S-0 and S-2<-- S-0 excitations are, respectively, electric-dipole forbidden and allowed. Attention is also given to aspects of the theory for singlet-singlet (pi(D)pi(D)*)(n(A)n(A))-->(pi(D)pi(D))(n(A)pi(A)*) EET with vibronic coupling. The theory for S-1+S-1-->S-2+S-0 is illustrated via the results of some model calculations for two C=S chromophores. For each chromophore, the calculations treat explicitly the valence-shell p pi atomic orbitals and a sulphur lone-pair atomic orbital. The results of the calculations highlight the nature of the primary contributors to the vibronic coupling component of the electronic EET matrix element, namely Coulombic-type terms. The theory also shows that a Coulombic term is the primary contributor to the vibronic coupling component for singlet-singlet (pi(D)pi(D)*)(n(A)n(A)) -->(pi(D)pi(D))(n(A)pi(A)*) EET.