  Gradient expansions in quantum transport equations of a Kadanoff-Baym form
have been reexamined. We have realized that in a consistent approach the
expansion should be performed also inside of the self-energy in the scattering
integrals of these equations. In the first perturbation order this internal
expansion gives new correction terms to the generalized Boltzman equation.
These correction terms are found here for several typical systems. Possible
corrections to the theory of a linear response to weak electric fields are also
discussed.
