When a pregalactic gas of H and He is heated and reionized, as by a shock wave occurring in the nonlinear collapse of density fluctuations or in the case of explosions in the IGM, the gas cools radiatively and recombines out of equilibrium. The temperature drops faster than the ions can recombine. When the temperature falls below 104K, the residual electron concentration is large enough, as a result, to form H− ions which form H2 molecules, via (H + e → H− + hν) and (H + H− → H2 + e). Molecules also form via (H+ + H → H2+ + hν) and (H2+ + H → H2 + H+). As a consequence, H2 can form with a sufficient concentration (∼10−3) to cool the gas further, by rot-vibrational line excitation and the formation process itself, to ∼102K. This has an important effect on the Jeans mass and fragmentation. We show some illustrative results below for the time-dependent cooling and non-equilibrium recombination and molecule formation. The three cases are as follows: (1) isochoric cooling at hydrogen number density 1 cm−3; (2) isochoric cooling at 3×107 cm−3; (3) isobaric cooling starting at initial density 1 cm−3. At high densities, molecular cooling is suppressed.