  We study the interactions of the discrete states with nonzero ghost number in
$c=1$ two-dimensional ($2D$) quantum gravity. By using the vertex operator
representations, it is shown that their interactions are given by the structure
constants of the group of the area preserving diffeomorphism similar to those
of vanishing ghost number. The effective action for these states is also worked
out. The result suggests the whole system has a BRST-like symmetry.
