A process is provided for preparing calcium carbonate hydroxodialuminates which have a hexagonal platelet-shaped crystal habit and are of the formula (A): CamAl2(OH)6+2(m−1)An*nH2O  (A) where m=3.5 to 4.5 and An=carbonate which may be partly replaced by perchlorate and/or trifluoromethanesulfonate (triflate) and n=0 to 6, comprising the steps of reacting calcium oxide or calcium hydroxide with optionally activated aluminum oxohydroxide or aluminum hydroxide and simultaneously or subsequently with a carbonate source consisting of carbon dioxide or alkali metal (bi)carbonate and optionally further reacting the product obtained in step (a) with perchloric acid and/or trifluoromethanesulfonic acid or optionally calcining the product obtained in step (a) at 200° C. to 900° C. and subsequently exchanging ions in the presence of a perchlorate and/or triflate salt, optionally in the presence of alkali metal (bi)carbonate, in water. The present invention further relates to the aluminates thus obtained in compositions and stabilizer systems and to the use thereof.