Genome replication of positive strand RNA viruses requires the production of a complementary negative strand RNA that serves as a template for synthesis of more positive strand progeny. Structural RNA elements are important for genome replication, but while they are readily observed in the positive strand, evidence of their existence in the negative strand is more limited. We hypothesized that this was due to viruses differing in their capacity to allow this latter RNA to adopt structural folds. To investigate this, ribozymes were introduced into the negative strand of different viral constructs; the expectation being that if RNA folding occurred, negative strand cleavage and suppression of replication would be seen. Indeed, this was what happened with hepatitis C virus (HCV) and feline calicivirus (FCV) constructs. However, little or no impact was observed for chikungunya virus (CHIKV), human rhinovirus (HRV), hepatitis E virus (HEV), and yellow fever virus (YFV) constructs. Reduced cleavage in the negative strand proved to be due to duplex formation with the positive strand. Interestingly, ribozyme-containing RNAs also remained intact when produced in vitro by the HCV polymerase, again due to duplex formation. Overall, our results show that there are important differences in the conformational constraints imposed on the folding of the negative strand between different positive strand RNA viruses.