In recent experiments of Bose-Einstein condensation of a magnetically trapped dilute alkaline atomic gas, the nonequilibrium process of thermalization into the condensed state has been observed in a reasonably long time scale. This presents a new challenge to develop a theory to treat strongly space-time dependent nonequilibrium processes. In this paper, we present a nonequilibrium formulation of Bose-Einstein condensed states in the field theoretical framework of thermo-field dynamics. By use of an effective Hamiltonian method, a quasi-particle field equation is derived. This equation contains information regarding the renormalized energy, decay width and time-variation of particle distributions. It is shown that, in the present formulation, the strong space-time dependence can be treated, even including quantum corrections, as the use of the quasi-particle field equation enables us to factorize double-time functions of the self-energy.