We report a study of the exciton dynamics in 1,1'-diethyl-3,3'-bis(sulforpropyl)-5,5',6,6' -tetrachlorobenzimidacarbocyanine (BIC) J-aggregates in water solution at room temperature by third-order nonlinear optical spectroscopy and numerical simulations based on exciton theory. The temporal profiles of the transient grating signals depend strongly on the excitation intensity as a result of exciton-exciton annihilation. On the other hand, the peak shift measurement gives information on the fluctuations of the transition frequency of the system. The peak shift decays with time constants of 26 and 128 fs. There is no finite peak shift on a longer time scale. The electronic state of J-aggregates is described by a Frenkel exciton Hamiltonian, and the exciton population relaxation processes is described by Redfield equations. Based on the numerical simulations, the peak shift data can only be explained even qualitatively when both exchange narrowing and exciton relaxation process are included in the model. The 128-fs component is assigned to a "hopping" time between exciton units. We confirmed that while the static disorder within an exction state that is partially delocalized due to static disorder is exchange-narrowed, the exchange narrowing of the dynamical disorder is not complete but appears as lifetime broadening, which competes with the exchange narrowing of the fluctuations. The effect of the exciton relaxation on the absorption spectrum is discussed.