  We consider correlation functions of operators and the operator product
expansion in two-dimensional quantum gravity. First we introduce correlation
functions with geodesic distances between operators kept fixed. Next by making
two of the operators closer, we examine if there exists an analog of the
operator product expansion in ordinary field theories. Our results suggest that
the operator product expansion holds in quantum gravity as well, though special
care should be taken regarding the physical meaning of fixing geodesic
distances on a fluctuating geometry.
