The peculiar two-step ordering kinetics, discovered recently in time-resolv
ed X-ray experiments on the Cu3Au(001) surface after a temperature quench t
o the ordered phase is analyzed within the time-dependent Ginzburg-Landau t
heory. Our model accounts for both the fast propagation of an ordering wave
into the bulk, initiated by Au-surface segregation, and a time-delayed pro
pagation of lateral order from the bulk to the surface. We also discuss fur
ther effects predicted by our theory, like the appearance of a characterist
ic penetration depth of the ordering wave and a secondary relaxation in its
amplitude, which have not yet been detected experimentally.