Aims. To demonstrate the time-approach to equilibrium of H 2 -formation and protonation in models of diffuse or H I interstellar gas clouds previously published by the author. Methods. The microscopic equations of H 2 -formation and protonation are integrated numerically over time in such a manner that the overall structures evolve self-consistently under benign conditions. Results. The equilibrium H 2 formation timescale in an H I cloud with N(H) ≈ 4 × 10 20 cm −2 is 1−3 × 10 7 yr, nearly independent of the assumed density or H 2 formation rate on grains, etc. Attempts to speed up the evolution of the H 2 -fraction would require densities well beyond the range usually considered typical of diffuse gas. The calculations suggest that, under benign, quiescent conditions, H 2 in the diffuse ISM formation of H 2 is favored in larger regions having moderate density, consistent with the rather high mean kinetic temperatures measured in H 2 , 70−80 K. Formation of H 3 + is essentially complete when H 2 -formation equilibrates but the final abundance of H 3 + appears more nearly at the very last instant. Chemistry in a weakly-molecular gas has particular properties so that the abundance patterns change appreciably as gas becomes more fully molecular, either in model sequences or with time in a single model. One manifestation of this is that the predicted abundance of H 3 + is much more weakly dependent on the cosmic-ray ionization rate when n(H 2 )/n(H) < ∼ 0.05. In general, high abundances of H 3 + do not enhance the abundances of other species (e.g. HCO + ) but late-time OH formation proceeds most vigourously in more diffuse regions having modest density, extinction and H 2 fraction and somewhat higher fractional ionization, suggesting that atypically high OH/H 2 abundance ratios might be found optically in diffuse clouds having modest extinction.