Based on a deterministic mutation–selection model the concept of error thresholds is critically examined. It has often been argued that genetic information – for instance, an advantageous allele – can be selectively maintained in a population only if the mutation rate is below a certain limit, the error threshold, which is inversely related to the genome size. Here, I will show that such an inverse relationship strongly depends on the fitness model. To produce the error threshold, as given by Eigen (1971), requires that the fitness model is an extreme form of diminishing epistasis. The error threshold, in a strict sense, vanishes as epistasis changes from diminishing to synergistic. In the latter case even the usual definition of error thresholds becomes ambiguous. Initially, a finite sites model has been used to describe error thresholds. However, they can also be defined within the framework of the infinite sites model. I study both models in parallel and compare their properties as far as error thresholds are concerned. It is concluded that error thresholds possibly play a much less important role in molecular evolution than has often been assumed in the past.