  The non-Markoffian transport equations for the systems of cold Bose atoms
confined by a external potential both without and with a Bose-Einstein
condensate are derived in the framework of nonequilibrium thermal filed theory
(Thermo Field Dynamics). Our key elements are an explicit particle
representation and a self-consistent renormalization condition which are
essential in thermal field theory. The non-Markoffian transport equation for
the non-condensed system, derived at the two-loop level, is reduced in the
Markoffian limit to the ordinary quantum Boltzmann equation derived in the
other methods. For the condensed system, we derive a new transport equation
with an additional collision term which becomes important in the Landau
instability.
