  We investigate analytically the non-equilibrium spatial phase segregation
process of a mixture of alkali Bose-Einstein condensates. Two stages (I and II)
are found in analogy to the classical spinodal decomposition.
  The coupled non-linear Schr\"odinger equations enable us to give a
quantitative picture of the present dynamical process in a square well trap.
  Both time and length scales in the stage I are obtained.
  We further propose that the stage II is dominated by the Josephson effect
between different domains of same condensate different from scenarios in the
classical spinodal decomposition.
  Its time scale is estimated.

Condensed Matter