  We discuss physical spectra and correlation functions of topological minimal
models coupled to topological gravity. We first study the BRST formalism of
these theories and show that their BRST operator $Q=Q_s+Q_v$ can be brought to
$Q_s$ by a certain homotopy operator $U$, $UQU^{-1}=Q_s$ ($Q_s$ and $Q_v$ are
the $N=2$ and diffeomorphism BRST operators, respectively). The
reparametrization (anti)-ghost $b$ mixes with the supercharge operator $G$
under this transformation. Existence of this transformation enables us to use
matter fields to represent cohomology classes of the operator $Q$. We
explicitly construct gravitational descendants and show that they generate the
higher-order KdV flows. We also evaluate genus-zero correlation functions and
rederive basic recursion relations of two-dimensional topological gravity.
