The second-order induction energy in the symmetry-adapted perturbation theory is expressed in terms of electron densities and polarization propagators at zero frequency of the isolated monomers. This expression is used to derive many-body perturbation series with respect to the Moller-Plesset type correlation potentials of the monomers. Two expansions are introduced-one based on the standard Moller-Plesset expansion of electron densities and polarization propagators, and the second accounting for the so-called response or orbital relaxation effects, i.e., for the perturbation induced modification of the monomer’s Fock operators. Explicit orbital formulas for the leading perturbation corrections that correctly account for the response effects are derived through the second order in the correlation potential. Numerical results are presented for several representative van der Waals complexes-a rare gas atom and an ion Ar-Na+, Ar-Cl-, and He-F-; a polar molecule and an ion H2O-Na+ and H2O-Cl-; two polar molecules (H2O)2; and a rare gas atom and a polar molecule Ar-HCl and He-HCl. It is shown that in the above systems, the significance of the correlation part of the induction energy varies from a very important one in the complexes of rare gas atoms and ions to a practically negligible one in the complexes of rare gases with polar molecules.