A particularly suitable process for economic dewatering of moist organic material, especially of organic waste, essentially consists of forming heaps with a height of from 2 m to 4 m of the moist organic material, and blowing in air in an amount which suffices to maintain the growth of thermophilic bacteria which are present in the moist organic mass, and to remove the vapour which has formed. The invention also relates to the system for carrying out this process.