Process for producing polyamides that are stable during processing, by treating the polyamide during the solid-phase postcondensation process with a gas which comprises carrier gas (inert gas), water, and acid, or an anhydride or lactone or a mixture of these or, respectively, comprises ammonia, or amine, or a mixture of these, at a temperature from 130 to 200° C. and at a pressure of from 0.01 to 10 bar.