Organopolysiloxanes having aminoalkyl groups are prepared by (i) reacting (A) linear, cyclic or branched organopolysiloxanes with (B) aminoalkyl silanes having an SiC-bonded hydrocarbon radical comprising basic nitrogen and 2 or 3 hydrolyzable groups, or partial or full hydrolyzates thereof, in the presence of (C) basic catalysts and optionally (D) chain-terminating reagents, at a temperature of at least 60.degree. C., then, after the reaction (i), (ii) deactivating the catalysts (C) and (iii) cooling the product to a temperature below 60.degree. C. before, during or after the deactivation (ii) of the catalysts, with the proviso that the process is performed in at least two successive stirred tanks, the reaction (i) and the cooling (iii) proceeding separately in different stirred tanks.