  Some elaboration is given to the structure of physical states in 2D gravity
coupled to $C \leq 1$ matter, and to the chiral algebra ($w_{\infty}$) of
$C_{M} = 1$ theory which has been found recently, in the continuum approach, by
Witten and by Klebanov and Polyakov. It is shown then that the chiral algebra
is being realized as well in the minimal models of gravity ($C_{M}<1$), so that
it stands as a general symmetry of 2D gravity theories.
