  We study the BRST quantization of the 1+1 dimensional gravity model proposed
by Jackiw and Teitelboim and also the topological gauge model which is
equivalent to the gravity model at least classically. The gravity model
quantized in the light-cone gauge is found to be a free theory with a nilpotent
BRST charge. We show also that there exist twisted N=2 superconformal algebras
in the Jackiw-Teitelboim's model as well as in the topological gauge model. We
discuss the quantum equivalence between the gravity theory and the topological
gauge theory. It is shown that these theories are indeed equivalent to each
other in the light-cone gauge.
