The review considers two reactions discovered recently: (1) excision of the 3'-terminal nucleotide from the nascent DNA strand in the presence of relatively high concentrations of noncomplementary r/dNTPs or r/dNDPs (pseudopyrophosphorolysis), which is catalyzed by various DNA polymerases (DNAPs), and (2) excision of the 3'-terminal nucleotide from the nascent RNA strand, which is catalyzed by RNA polymerases (RNAPs) and stimulated by noncomplementary r/dNTPs. The mechanism of excision differs between DNAPs and RNAPs. With the former, the 3'-terminal nucleotide is excised in the presence of noncomplementary NTPs to yield dinucleoside 5',5"-tetraphosphate. With RNAPs, noncomplementary NTPs stimulate 3' --> 5' exonucleolytic cleavage of the nascent RNA. Data are reviewed on the possible role of pseudopyrophosphorolysis catalyzed by reverse transcriptase (RT) of the human immunodeficiency virus (HIV) in HIV resistance to nucleoside RT inhibitors, in particular, azidothymidine (AZT). Other mechanisms of RT resistance to nucleoside inhibitors are also discussed.