A special class of biochemical reactions involves a set of enzymes that generate additional copies of themselves and transfer heritable information from parent to progeny molecules, thus providing the basis for genetics and Darwinian evolution. Such a process has been realized with a pair of self-replicating RNA enzymes that undergo exponential amplification at a constant temperature. Exponential growth requires that the rate of production of new enzymes be directly proportional to the existing concentration of enzymes, which is the case for this system and provides a doubling time of ~20 min. However, the catalytic rate of the underlying enzymes is ~100-fold faster than the observed rate of replication. As in biological replication, other aspects of the system limit the generation time, chiefly the propensity of the substrate molecules to form nonproductive complexes that limit their availability for replication. An analysis of this and other kinetic properties of the self-replicating RNA enzymes reveals how exponential amplification is achieved and how the rate of amplification might be increased.