Abstract The formalism developed in Part I is applied to the pairwise δ-function potential. For this purpose the first-order perturbation caused by the δ-potential is expressed in terms of creation and annihilation operators. Splittings of energy levels are calculated for low excited states of three-, four-, and five-particle systems. The correlation diagrams are constructed to connect the energy levels of clusters corresponding to this nearly-nonrigid limit and those of the nearly-rigid molecules calculated in the harmonic approximation. The construction is carried out for an arbitrary pairwise interaction between three or four particles and for the Lennard-Jones potential in the case of the five-particle system.