Constitutive equations for a fluid are worked out to the order corresponding to the Burnett approximation of kinetic theory, using the method of time-dependent correlation functions. These equations describe effects such as normal stresses which are characteristic of non-Newtonian fluids. Coefficients of the various terms are identified as integrals of correlation functions; those associated with linear second-order terms involve space and time moments of the same two-point correlation functions which occur in the first-order theory, while the coefficients of nonlinear terms depend in addition on three-point correlation functions.