Liquid desiccant cooling systems are especially suitable for solar energy applications. The liquid desiccants can be regenerated at temperatures below 80 degrees C and the concentrated and diluted desiccants can easily be stored to provide a high energy storage capacity for air dehumidification and cooling. Special absorption processes are necessary to achieve an optimal air dehumidification and simultaneously a high energy storage capacity. The dominating effects on the absorption process are discussed in detail. For efficient dehumidification the temperature of the absorption process and the inlet concentration of the salt solution are of major importance. For a high energy storage capacity a high air to solution mass ratio is required to achieve great differences between salt inlet and outlet concentrations. A high mass ratio corresponds to a small desiccant flow. New dehumidifiers have been developed and tested, to achieve an efficient air dehumidification and high storage capacity. They dehumidify air by a very small flow of a hygroscopic aqueous salt solution, cg. LiCl-H2O in an internally cooled absorption process. Experimental results of air dehumidification and storage capacities are reported. Mass transfer coefficients, used in numerical models, have been identified by absorption experiments and enable the reliable sizing of dehumidifiers.