A novel catalyst system based on complexes of calcium which promote the catalytic asymmetric 1,4-addition reactions and [3+2] cycloaddition reactions of alpha-amino acid derivatives with alpha,beta-unsaturated carbonyl compounds have been developed. The reactions proceeded smoothly in the presence of 5-10 mol % of the chiral calcium catalyst to afford the desired adducts in high yields with high diastereo- and enantioselectivities. A wide range of alpha,beta-unsaturated esters and amides were applicable, and other glycine and even dl-alanine derivatives reacted with several alpha,beta-unsaturated carbonyl compounds to afford the corresponding substituted pyrrolodine derivatives in high yields with excellent diastereo- and enantioselectivities. In the reactions with dl-alanine derivatives, quaternary asymmetric carbons were constructed efficiently.