The Rayleigh-Schrodinger perturbation theory approach developed previously for evaluating nonadiabatic corrections to the adiabatic energy levels of a system of two coupled oscillators is generalized to the case of the so-called "mixed" representations which arise from the diabatic representation of a given problem by performing a unitary transformation on the diabatic potential energy matrix (the adiabatic representation is obtained as a special case with a purely diagonal potential energy matrix). Different representations provide different coupling conditions and, consequently, different bases for evaluation of the perturbation corrections, This is reflected, quite generally, in the convergence and summability properties of the perturbation series and can thus be used to improve the accuracy and stability of the perturbation calculations, The latter possibility is especially important in the case of closely coinciding levels. Model calculations have revealed that changing representations may allow the determination of the energies of these levels to a high degree of accuracy even in the case of strong perturbation resonances,