  We study the evolution of timelike geodesics for two dimensional black hole
spacetimes arising in string theory and general theory of relativity by solving
the Raychaudhuri equation for expansion scalar as an initial value problem. The
possibility of geodesic focusing/defocusing is then examined accordingly with
different settings of black hole parameters. In view of the geodesic
focusing/defocusing, the critical value of expansion scalar is also calculated
in each case. The effect of the charge and the cosmological constant on the
evolution of expansion scalar for timelike geodesics is discussed in detail.
