Transient nucleation is studied for a binary vapor of water and sulfuric acid, in which the acid is assumed to form a hydrate H2SO4 . 2H2O. The rate equation is solved numerically under the condition that only monomers of water and the hydrate exist initially, and it is found that (1) At the first stage the number densities of clusters with single acid molecule but containing more and more water molecules increase very rapidly. (2) Soon the rates of increase in the densities of those clusters slow down, then the densities of clusters with two arid molecules develop from the region around the valley in the contours of the reversible work of cluster formation. These observations seem to support the idea that in the analysis of steady state nucleation the population of clusters may be treated as in equilibrium with respect to exchange with water molecules in the vapor. (3) As for the effect of the difference in the formulas for the reversible work of cluster formation, the conventionally used formula and the one due to Nishioka and Mori, on the transient nucleation behavior, the conventionally used formula may cause significant errors when the critical nucleus obtained from it contains erroneous number of acid molecules. (4) The time lag to reach the steady state is found to be much longer than 1 ms, and it is not possible to continue the computer simulation up to the steady state in the present system.