An RNA‐dependent RNA polymerase purified from tobacco infected with cucumber mosaic virus catalyses the synthesis of (−) and (+) strands of the viral satellite RNA, CARNA 5, but fails to replicate the satellite RNA of peanut stunt virus (PSV). The enzyme replicates the genomic RNAs of the three principal cucumoviruses CMV. PSV and tomato aspermy virus (TAV) with varying efficiencies. The specificity with which CMV RdRp replicates different sequence‐unrelated RNA templates suggests that the site of their recognition requires secondary or higher level structural organization.