  The aim of this paper is to investigate well-posedness of the Cauchy problem
for the degenerate Zakharov system. Local well-posedness holds for anisotropic
Sobolev data by applying $U^2, V^2$ type spaces. We give the Schr\"odinger
initial data $H^{s_k, s'}$ and the wave data $H^{s_l, s'}$ where $s_k >
(d-1)/2, s_l > (d-2)/2, s_k - s_l = 1/2$ and $s' > 1/2$.
