For three decades, "conventional" nonlinear effects in asymmetric catalysis, commonly becoming apparent as a nonproportional relationship between the enantiomeric purity of the chiral catalyst and that of the chiral reaction product, have been extensively studied from both fundamental and practical perspectives and thoroughly reviewed. In contrast, this review is focused on dynamic nonlinear effects, with the catalyst systems exhibiting variation of enantioselectivity over the reaction course, caused by catalyst-product or catalyst-substrate interactions. Namely, such phenomena as asymmetric autoinduction, asymmetric autocatalysis, and asymmetric autoamplification are considered and the corresponding catalytic reactions are surveyed. Whenever available, data on the origins of the observed nonlinearities are presented. Several kinetic schemes, illustrating the nonlinear ee variation over the reaction course, are considered. Possible implications of dynamic nonlinear effects in asymmetric catalysis in the problem of biological homochirality on Earth are discussed briefly.