A general, Brønsted acid-catalyzed hetero-Michael addition of nitrogen, oxygen, and sulfur nucleophiles.

[reaction: see text] Strong Brønsted acids such as bis(trifluoromethanesulfon)imide catalyze the hetero-Michael addition of carbamates, alcohols, and thiols to alpha,beta-unsaturated ketones, alkylidene malonates, and acrylimides. Scope, reaction rates, and yields are superior to comparable Lewis acid-catalyzed processes.