On Nonlinear Dynamics of Fluctuations*>

A projection-operator method is developed for renormalizing kinetic coefficients by the nonlinear interaction between macroscopic modes in a nonlinear Langevin equation which is often used in studying anomalous transport phenomena near critical points and anomalous transport coefficients in two dimension; It is shown that the renormalization term is given by the time correlation of a new fluctuating force. Other theories are derived from this expres-sion by making approximations. A relation between the Langevin fluctuating force and the transport fluctuating force is derived to clarify the relation between the Fokker-Planck equa-tion approach by Green and Zwanzig and the linear equation-of-motion approach by one of the authors