Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organ- isms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation- induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation ac- cumulation and demographic stochasticity). Here we analyze a dynamical system describing the intracel- lular amplification of viral RNA genomes evolving on a single-peak fitness landscape focusing on three cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and error threshold, governed by transcritical bifurcations that depend on parameters α(parameter introducing the mode of replication), replicative fitness of mutants ( k 1 ), and on the spontaneous degradation rates of the sequences ( ). Our results relate the error catastrophe with lethal mutagenesis in a model with continuous populations of viral genomes. The former case involves dominance of the mutant sequences, while the latter, a deterministic extinction of the viral RNAs during replication due to increased mutation. For the lethal case the critical mutation rate involving lethal mu- tagenesis is μc = 1 −ε/ √ α. Here, the SMR involves lower critical mutation rates, being the system more robust to lethal mutagenesis replicating closer to the GR mode. This result is also found for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the error threshold once the replication mode surpasses a threshold given by √ α= /k 1 .