We study the spontaneous phase separation of a binary mixture in the p
resence of a flat wall, focusing on the early stage of the demixing ki
netics. Based on a Ginzburg-Landau type approach, we show the existenc
e of novel unstable concentration waves with wave vectors (k) over rig
ht arrow(parallel to) parallel to the wall, which are characterized by
a surface dispersion relation omega(s)(k(parallel to)) and amplitudes
(s) over bar decaying exponentially into the bulk. The surface modes
are superimposed on the laterally averaged concentration profile and a
re directly observable by experiment, if the wall right after a quench
does not favor any of the two components of the mixture.