  We present a derivation of a Boltzmann equation for the QCD plasma, starting
from the quantum field equations. The derivation is based on a gauge covariant
gradient expansion which takes consistently into account all possible
dependences on the gauge coupling assumed to be small. We point out a
limitation of the gradient expansion arising when the range of the interactions
becomes comparable with that of the space-time inhomogeneities of the system.
The method is first applied to the case of scalar electrodynamics, and then to
the description of long wavelength colour fluctuations in the QCD plasma. In
the latter case, we recover B\"odeker's effective theory and its recent
reformulation by Arnold, Son and Yaffe. We discuss interesting cancellations
among various collision terms, which occur in the calculation of most transport
coefficients, but not in that of the quasiparticle lifetime, or in that of the
relaxation time of colour excitations.
