A macroporous adsorbent comprising pores having a pore volume (V.sub.m) and a mean pore diameter (d.sub.m) such that: V.sub.m.gtoreq.1 cc.g.sup.-1 and d.sub.m.gtoreq.1 .mu.m, V.sub.m and d.sub.m being determined by mercury porosimetry; their manufacturing process using a spheronization and freeze-drying technique; and their use for separating or purifying gases, such as air, synthesis gases or hydrocarbons, especially olefins.