Journal of Statistical Physics, Vol. 32, No. 1, 1983. p. 53-69.
If the kinetic equation of a macroscopic system is expanded with respect to the velocity in terms of orthogonal functions, e.g., in terms of Hermite functions, one obtains an infinite hierarchy of equations for the expansion coefficients. Grad's method consists in truncating this hierarchy and investigating the remaining finite system. In this paper we set up conditions under which this procedure is rigorously justified in case of the Fokker-Planck equation.