Energy formulae for two-particle Klein-Gordon systems subjected to Coulomb and Yukawa potentials are derived to first 1/N-order. The energies obtained in this manner incorporate the influence of the mass-asymmetry via the parameter δ = (m₁² − m₂²)². Certain Coulomb-inspired extrapolations to Dirac-particle systems, having the meaning of dominant contributions, are taken into account. Numerical results are presented.