It has been considered since the first discovery of a high-T(c) cuprate that an antiferromagnetic (AF) state and a superconducting (SC) state are separated in it. However, it is very intriguing that the coexistence of the AF and SC states has recently been observed in HgBa(2)Ca(4)Cu(5)O(12+) (Hg-1245). Moreover, it is very novel that this coexistence of these two states appears if the SC-transition temperature T(c) is higher than the AF-transition temperature T(N). The mode-mode coupling theory can provide a clear elucidation of this novel phenomenon. A key point of this theory is that the AF susceptibility consists of the random-phase-approximation (RPA) term and the mode-mode coupling one. The RPA term works to make a positive contribution to the emergence of the antiferromagnetic critical point (AF-CP). In contrast, the mode-mode coupling term works to make a negative contribution to the emergence of the AF-CP. However, the growth of the SC-gap function in the d(x(2)-y(2))-wave SC state works to suppress the negative contribution of the mode-mode coupling term to the emergence of the AF-CP. Moreover, the effect of SC fluctuations near the SC-transition temperature T(c) suppresses the mode-mode coupling term of the AF susceptibility that works to hinder the AF ordering. For these two reasons, there is a possibility that the d(x(2)-y(2))-wave SC state is likely to promote the emergence of the AF-CP. Namely, the appearance of the above-mentioned novel coexistence of the AF and SC states observed in Hg-1245 can be explained qualitatively on the basis of this idea.