By pretreating simian virus 40-infected BSC-1 cells with glucosamine, [(3)H]uridine labeling of both cellular and viral RNA can be halted instantaneously by addition of cold uridine. We have studied the fate of pulse-labeled viral RNA from cells at 45 h postinfection under these conditions. During a 5-min period of labeling, both the messenger and nonmessenger regions of the late strand were transcribed. After various chase periods, nuclear viral species which sediment at 19, 17.5, and 16S were observed. Nuclear viral RNA decays in a multiphasic manner. Of the material present at the beginning of the chase period, 50% was degraded rapidly with a half-life of 8 min (initial processing). This rapidly degraded material was that fraction of the late strand which did not give rise to stable late mRNA species. Forty percent was transported to the cytoplasm, and 10% remained in the nucleus as material which sedimented in the 2 to 4S region. These 2 to 4S viral RNAs had a half-life of 3 h, and hybridization studies suggest that they are in part coded for by the late-strand nonmessenger region and are derived from the initial nuclear processing step. Another part is coded for by the late-strand messenger region and may be generated by some subsequent nuclear cleavages of 19S RNA into 17.5 and 16S RNAs. Transport of nuclear viral RNA into the cytoplasm was detected after a 5-min pulse and a 7-min chase. The maximum amount of labeled viral RNA was accumulated in the cytoplasm after a 30-min to 1-h chase. At least two viral cytoplasmic species were observed. Kinetic data suggest that 19S RNA is transported directly from the nucleus. Whether cytoplasmic 16S is formed by cleavage of 19S RNA in the cytoplasm is not clear. The half-lives of cytoplasmic 19 and 16S RNAs can be approximated as 2 and 5 h, respectively.