The full details of a catalytic asymmetric aza-Michael reaction of methoxylamine promoted by rare earth-alkali metal heterobimetallic complexes are described, demonstrating the effectiveness of Lewis acid-Lewis acid cooperative catalysis. First, enones were used as substrates, and the 1,4-adducts were obtained in good yield (57-98%) and high ee (81-96%). Catalyst loading was successfully reduced to 0.3-3 mol % with enones. To broaden the substrate scope of the reaction to carboxylic acid derivatives, alpha,beta-unsaturated N-acylpyrroles were used as monodentate, carboxylic acid derivatives. With beta-alkyl-substituted N-acylpyrroles, the reaction proceeded smoothly and the products were obtained in high yield and good ee. Transformation of the 1,4-adducts from enones and alpha,beta-unsaturated N-acylpyrroles afforded corresponding chiral aziridines and beta-amino acids. Detailed mechanistic studies, including kinetics, NMR analysis, nonlinear effects, and rare earth metal effects, are also described. The Lewis acid-Lewis acid cooperative mechanism, including the substrate coordination mode, is discussed in detail.