This paper is concerned with a further exploration of the approach taken for the problem of anomalous spin diffusion in the isotropic ferromagnetic Heisenberg system in our previous work. First the approach is extended to the case of an isotropic antiferromagnetic spin system. Despite some complications which suggest a possible modification of the approach and lead to alternative self-consistent formulations other than the original one, we have obtained a unique time-scale characterizing the relaxation which grows as κ-3/2 near and above the Neel point, where κ is the reciprocal correlation range of spin fluctuations (critical slowing-down). This time-scale is in better accord with the recent neutron critical scattering experiment of Torrie on MnF2 than that of the conventional theory which behaves as κ-2. This result together with that of the ferromagnetic case are applied to the problems of NMR and ESR linewidths near the magnetic transitions. A simple method of obtaining the characteristic time-scales knowing the existence of the critical slowing-down is presented, and the characteristic time-scales in ferro- and antiferromagnetic cases are found to be determined by the long wavelength parts of the second moments of frequency spectra of appropriate spin relaxation functions. In the presence of uniaxial anisotropy the above treatments do not apply and the conventional theory of critical slowing-down appears to be adequate.