RNA-catalyzed RNA replication is widely considered a key step in the emergence of life's first genetic system. However, RNA replication can be impeded by the extraordinary stability of duplex RNA products, which must be dissociated for re-initiation of the next replication cycle. Here, we have explored rolling circle synthesis (RCS) as a potential solution to this strand separation problem. We observe sustained RCS by a triplet polymerase ribozyme beyond full-length circle synthesis with strand displacement yielding concatemeric RNA products. Furthermore, we show RCS of a circular Hammerhead ribozyme capable of self-cleavage and re-circularization. Thus, all steps of a viroid-like RNA replication pathway can be catalyzed by RNA alone. Finally, we explore potential RCS mechanisms by molecular dynamics simulations, which indicate a progressive build-up of conformational strain upon RCS with destabilization of nascent strand 5'- and 3'-ends. Our results have implications for the emergence of RNA replication and for understanding the potential of RNA to support complex genetic processes.