It is shown that the multipole expansion of each order of the polarization series converges for large enough intermol. distances when finite basis sets of Gaussian or Slater-type functions are used to approx. mol. response properties. Convergence of the multipole expansion for each order of the polarization series does not imply convergence of the polarization series itself. A corresponding convergence condition is extd. from the general perturbation theory in a finite-dimensional space and is applied to the H + H+ problem.