  We present the (1+1)-dimensional description of the algebraically special
class of space-times of 4-dimensions. It is described by the (1+1)-dimensional
Yang-Mills action interacting with matter fields, with diffeomorphisms of
2-surface as the gauge symmetry. Parts of the constraints are identified as the
gauge fixing condition. We also show that the representations of
$w_{\infty}$-gravity appear naturally as special cases of this description, and
discuss the geometry of $w_{\infty}$-gravity in term of the fibre bundle.
