Charge transfer processes for double-electron colliding systems H++He and He2++He have been studied by using the asymptotic two-state atomic expansion method developed recently. Our results for the cross sections of electron capture are in good agreement with those given by the boundary-corrected first-order Born (B1B) approximation and experimental data in high-intermediate energies, and in the low-intermediate energies the present results are better than those obtained by the B1B approximation. Finally, we point out that the reason that capture cross sections predicted by first-order perturbation theory are in poor agreement with experimental data.