A granular sorption material including a plurality of porous granules formed by buildup agglomeration for separation, especially absorption, of harmful gases, especially of SOX and/or HCl, from offgases of thermal processes. The granules containing greater than 80% by weight, and preferably greater than 95% by weight, of Ca(OH)2 and/or CaCO3 based on the dry mass. The granules having a dry apparent density ρ, determined by means of an apparent density pycnometer, of 0.5 to 1.2 kg/dm3, preferably 0.7 to 1.1 kg/dm3, and/or a porosity of 45% to 73% by volume, preferably 55% to 65% by volume, and have especially been increased in porosity. A process for producing the granular sorption material, in which pores are introduced into the granules by means of a porosity agent during the production.