Accurate numerical methods are applied to the vibronic problem resulting from bvo interacting intGI"86cting hRrInonlc cuI'ves. 7%"o GXRInples Rle considered, corresponding to either degenerate or nondegenerate electronic states. The energies are obtained ruth (a) the zerothorder Born-Oppenheimer appxoximation; (b) the so-called adiabatic approximation, which includes the di, agonal corrections to (a); (c) the full vibronic procedure. Several featuxes in the correlation diagrams giving tIM eneI'gie8 Rs R function of the configuration-intGI'action Matrix element aI'e given an explanation.We also note that, in the model treated here, inclusion of the diRgonRl corI'Gctlons does not always lead to Rn lmproveInent of the eneI'gies,