In the development of Thermo Field Dynamics (the quantum field theory at finite temperature and density), Prof. Mancini acted as one of the originators and played the important role for its birth through the work of superconductivity. Recent development of the Bose‐Einstein condensation in the dilute alkaline atomic gas enables us to investigate deeply the quantum coherence in bose and fermi particle systems, and gives us a plenty of experimental data even for the problem in nonequilibrium formation of the condensate. There the relaxation time is reasonably slow to make the laboratory observation possible. In this talk, we will show that Thermo Field Dynamics gives us a reasonable approximation scheme to describe time‐dependent ordered states with spatial inhomogeniety by use of a single‐time quasi‐particle field equation, which contains the information of the spatial and temporal dependent order parameter, particle energy and particle distribution. © 2003 American Institute of Physics