We study the kinetics of absorption of water in Portland cement concretes added with 60, 70 and 80% of granulated blast furnace slag (GGBS) cured in water and at open air and preheated at 50 and $100^{circ}C$. A mathematical model is presented that allows describing the process not only in early ages where the capillary sorption is predominant but also for later and long times where the diffusive processes through the finer and gel pores are considered. The fitting of the model by computerized methods enables us to determine the parameters that characterize the process: i.e., the sorptivity coefficient (S) and diffusion coefficient (D). This allows the description of the process for all times and offers the possibility to know the contributions of both, the diffusive and capillary processes. The results show the influence of the curing regime and the preheating temperature on the behavior of GGBS mortars.