  General solution of RG equations in the framework of background perturbation
theory is written down in the large N_c limit. A simplified (model)
approximation to the general solution is suggested which allows to write
beta(alpha) and alpha(beta) to any loop order. The resulting alpha_B(Q^2)
coincides asymptotically at large $|Q^2|$ with standard (free) alpha_s,
saturates at small Q^2 and has poles at time-like Q^2 in agreement with
analytic properties of physical amplitudes in the large N_c limit.
