In the Peri-Adriatic Apulia Carbonate Platform (southern ltaly), late Cretaceous karst bauxites mark an emergence period during a wet tropical climate. Bauxite formed through clay accumulation in the karst, ''in situ'' bauxitization and late formation of iron-rich concretions in a water-unsaturated pedogenic environment. The concretions, which are geochemical recorders of the environment of formation, have a large core of Al-hematite surrounded by a cortex of alternating Al-hematite and boehmite. Boehmite forms instead of Al-hematite at lower water activity values. Using a model of molecular diffusion and assuming the fluid flow negligible, the time necessary for growth of the concretions has been calculated. The average-sized core grew in ~180 ka. The Al-hematite accretionary band grew in ~8 ka whereas the boehmite accretionary band grew in ~4.5 ka. The average bulk concretions possibly formed in 300-400 ka. The growth of the concretions is assumed to be a two-stage process. In the first stage, the core grew in a relatively long period of wet tropical climate. In the second stage, drier conditions favouring boehmite stability alternated to a wetter climate favouring Al-hematite stability. The growth of the bulk concretions is consistent with the Earth's long eccentricity cycle.