Abstract. -It is a long-standing question in origin-of-life research whether the information content of replicating molecules can be maintained in the presence of replication errors. Extending standard quasispecies models of non-enzymatic replication, we analyze highly specific enzymatic self-replication mediated through an otherwise neutral recognition region, which leads to frequency-dependent replication rates. We find a significant reduction of the maximally tolerable error rate, because the replication rate of the fittest molecules decreases with the fraction of functional enzymes. Our analysis is extended to hypercyclic couplings as an example for catalytic networks.Introduction. -According to the RNA world hypothesis [1], prebiotic biochemical life is thought to have emerged through four steps: starting from the primordial non-enzymatic synthesis of nucleotides and their subsequent non-enzymatic polymerization into random RNA, which in a third step would non-enzymatically replicate, natural selection would finally produce a set of functional RNA enzymes (ribozymes), establishing exponential growth and initiating RNA evolution. Despite considerable experimental progress [2,3], as of today no truely self-replicating system has been evolved according to this hypothetic schedule. To assess its intrinsic plausibility, theory has mainly focused on the third step, usually based on the Eigen model [4] for prebiotic evolution: here, autocatalytic self-replication of L-nucleotide sequences proceeds non-enzymatically via stepwise template-directed polymerization, with a non-negligible error probability µ per single nucleotide. Assuming that one specific "master" template replicates with the highest rate α > 1, while all other sequences have unit replication rate, it is found that faithful replication of the master is possible only for error probabilities smaller than a critical value µ c ≈ ln α/L. In this regime, the population in sequence space is concentrated about the master in a rather broad distribution, giving rise to the notion of a "quasispecies". Larger values µ > µ c lead to a delocalized state with completely random sequences in the population. Many aspects of the