The mechanism of Lewis acid catalysed hetero-Michael addition reactions of weakly basic nucleophiles to alpha,beta-unsaturated ketones was investigated. Protons, rather than metal ions, were identified as the active catalysts. Other mechanisms have been ruled out by analyses of side products and of stoichiometric enone-catalyst mixtures and by the use of radical inhibitors. No evidence for the involvement of pi-olefin-metal complexes or for carbonyl-metal-ion interactions was obtained. The reactions did not proceed in the presence of the non-coordinating base 2,6-di-tert-butylpyridine. An excellent correlation of catalytic activities with cation hydrolysis constants was obtained. Different reactivities of mono- and dicarbonyl substrates have been rationalised. A (1)H NMR probe for the assessment of proton generation was established and Lewis acids have been classified according to their propensity to hydrolyse in organic solvents. Brønsted acid-catalysed conjugate addition reactions of nitrogen, oxygen, sulfur and carbon nucleophiles are developed and implications for asymmetric Lewis acid catalysis are discussed.