Some preliminary numerical results for the eigenvalue spectra and the time-correlation functions computed from the formulas derived in the preceding paper (paper II) are presented. First, it is claimed that certain conditions must be imposed on the translational and rotatory friction coefficients ζt and ζr of each of the sub-bodies comprising the model. The parameter ζt must lie in the range over which the diffusion matrix is positive definite. For the present model, the eigenvalues λ01,k in the lowest branch of the spectrum for the diffusion operator may possibly become negative at small wave numbers k because of the preaveraging approximation used. However, it is possible to make λ01,0 very small in magnitude, and thus to neglect it, by choosing ζr properly. For flexible chains, this enables one to remove the negative eigenvalues completely and recover the Rouse–Zimm values for λ01,k at small k in the coil limit in a very good approximation. Then, after the examination of the accuracy of the block-diagonal approximation, numerical results for the eigenvalues λjL,k (L=1,2;‖j‖≤L) in this approximation are presented, taking, as examples of flexible chains, isotactic and syndiotactic polystyrenes and isotactic and syndiotactic poly(methyl methacrylate)s, and as an example of stiff chains DNA all with proper assigned values of the model parameters. An empirical noncrossing rule is found. With these eigenvalues, the time-correlation functions relevant to the dielectric susceptibility are computed for the flexible chains, and the ones relevant to the fluorescence polarization anisotropy for DNA. The associated correlation times are also estimated, and a good agreement with experiment is found. Finally, a detailed discussion of some general aspects of the present theory is given. In the Appendix, an interpolation formula for the mean reciprocal distance between two subbodies is given.