Abstract: In a process and apparatus of conditioning an airstream, the airstream is contacted with a liquid desiccant absorber in each of at least two stages. The same apparatus used as an evaporator to reconcentrate the desiccant. The desiccant for each said stage is cooled or heated externally to the absorber or evaporator using an external source of cooling supplied with a common cooling or heating fluid at each stage. The desiccant flows between the stages counter-current to the flow of the airstream such that at each step the concentration of the desiccant is reduced or increased by contact with the airstream so that the concentration in each stage is distinct from the concentration of the desiccant in the previous stages.