A population of RNA molecules that catalyze the template directed ligation of RNA substrates was made to evolve in a continuous manner in the test tube. A simple serial transfer procedure was used to achieve approximately 300 successive rounds of catalysis and selective amplification in 52 hours. During this time, the population size was maintained against an overall dilution of 3 X 10²⁹⁸ . Both the catalytic rate and amplification rate of the RNAs improved substantially as a consequence of mutations that accumulated during the evolution process. Continuous in vitro evolution makes it possible to maintain laboratory "cultures" of catalytic molecules that can be perpetuated indefinitely.